Pub Date : 2023-02-06DOI: 10.21136/CMJ.2023.0005-22
E. Milovanovic, Ş. B. Bozkurt Altindağ, M. Matejic, I. Milovanovic
Let G = (V, E), V = {v1, v2, …, vn}, be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≽ d2 ≽ … ≽ dn. Denote by A and D the adjacency matrix and diagonal vertex degree matrix of G, respectively. The signless Laplacian of G is defined as L+ = D + A and the normalized signless Laplacian matrix as r(G)=γ2+/γn+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$rleft( G right) = gamma _2^ + /gamma _n^ + $$end{document}. The normalized signless Laplacian spreads of a connected nonbipartite graph G are defined as l(G)=γ2+−γn+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$lleft( G right) = gamma _2^ + - gamma _n^ + $$end{document}, where γ1+⩾γ2+⩾...⩾γn+⩾0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma _1^ + geqslant gamma _2^ + geqslant ldots geqslant gamma _n^ + geqslant 0$$end{document} are eigenvalues of ℒ+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{cal L}^ + }$$end{document}. We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower bound on the signless Laplacian spread.
设G=（V，E），V={v1，v2，…，vn}是一个具有n个顶点、m条边和一系列顶点度d1≽d2 8829…8829；dn的简单连通图。用A和D分别表示G的邻接矩阵和对角顶点度矩阵。G的无符号拉普拉斯算子定义为L+=D+A，归一化无符号拉普拉斯矩阵定义为r（G）=γ2+/γn+documentclass[12pt]｛minimal｝usepackage｛amsmath｝use package｛wasysym｝ usepackage{amsfonts｝usapackage｛amssymb｝userpackage｛amsbsy｝usepackage｛mathrsfs｝ use package{upgek｝setlength｛doddsedmargin｝｛-69pt｝begin｛document｝$rleft（Gright）=gamma _2^+/gamma _n^+$$结束｛文档｝。连通的非二分图G的归一化无符号拉普拉斯展开定义为l（G）=γ2+γn+documentclass[12pt]｛minimal｝usepackage｛amsmath｝use package{wasysym｝ usepackage{amsfonts｝ use package｛amssymb｝ usapackage｛amsbsy｝usepackage｛mathrsfs｝usapackage{upgeek｝setlength｛oddsidemargin｝｛-69pt｝boot｛document｝$lleft（Gright）=gamma _2^+-gamma _n^+$end{document}，其中γ1+γ2+γn+⩾0documentclass[12pt]｛minimal｝usepackage｛amsmath｝usepackage｛wasysym｝ usepackage{amsfonts｝usecpackage{amssymb｝ucepackage{hamsbsy｝usepackage｛mathrsfs｝userpackage｛upgeeek｝setlength｛doddsidemargin｝｛-69pt｝ begin｛document｝$gamma _1^+geqslantgamma _2^+ geqslantldotsgeqslant gamma _n^+getqslant 0$end｛ℒ+documentclass[12pt]｛minimal｝ usepackage｛amsmath｝ use package｛｛wasysym｝usepackage{amsfonts} usepackage{amssymb｝ userpackage{amsbsy｝usepackage{mathrsfs｝ user package{upgek｝setlength｛doddsedmargin｝｛-69pt｝ begin｛document｝$$｛cal L｝^+｝$end｛document｝。我们为连通图的归一化无符号拉普拉斯展开建立了清晰的下界和上界。此外，我们给出了无符号拉普拉斯展开的一个更好的下界。
{"title":"On the signless Laplacian and normalized signless Laplacian spreads of graphs","authors":"E. Milovanovic, Ş. B. Bozkurt Altindağ, M. Matejic, I. Milovanovic","doi":"10.21136/CMJ.2023.0005-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0005-22","url":null,"abstract":"Let G = (V, E), V = {v1, v2, …, vn}, be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≽ d2 ≽ … ≽ dn. Denote by A and D the adjacency matrix and diagonal vertex degree matrix of G, respectively. The signless Laplacian of G is defined as L+ = D + A and the normalized signless Laplacian matrix as r(G)=γ2+/γn+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$rleft( G right) = gamma _2^ + /gamma _n^ + $$end{document}. The normalized signless Laplacian spreads of a connected nonbipartite graph G are defined as l(G)=γ2+−γn+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$lleft( G right) = gamma _2^ + - gamma _n^ + $$end{document}, where γ1+⩾γ2+⩾...⩾γn+⩾0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma _1^ + geqslant gamma _2^ + geqslant ldots geqslant gamma _n^ + geqslant 0$$end{document} are eigenvalues of ℒ+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{cal L}^ + }$$end{document}. We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower bound on the signless Laplacian spread.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"499 - 511"},"PeriodicalIF":0.5,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48304773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-06DOI: 10.21136/CMJ.2023.0144-22
V. Bojković, Jovana Nikolić, M. Zekic
It is clear that every rational surgery on a Hopf link in 3-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the 3-sphere.
{"title":"A note on rational surgeries on a Hopf link","authors":"V. Bojković, Jovana Nikolić, M. Zekic","doi":"10.21136/CMJ.2023.0144-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0144-22","url":null,"abstract":"It is clear that every rational surgery on a Hopf link in 3-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the 3-sphere.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"603 - 611"},"PeriodicalIF":0.5,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46978568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-02DOI: 10.21136/CMJ.2023.0132-22
D. Jadhav, R. Deore
We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to 2n-conjecture. We determine that the 2n-conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least n − 1 nonzero entries.
{"title":"A geometric construction for spectrally arbitrary sign pattern matrices and the 2n-conjecture","authors":"D. Jadhav, R. Deore","doi":"10.21136/CMJ.2023.0132-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0132-22","url":null,"abstract":"We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to 2n-conjecture. We determine that the 2n-conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least n − 1 nonzero entries.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"565 - 580"},"PeriodicalIF":0.5,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43215503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-02DOI: 10.21136/CMJ.2023.0130-22
Anass Assarrar, N. Mahdou, Ünsal Tekir, Suat Koç
Recently, motivated by Anderson, Dumitrescu’s S-finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S-coherent rings, which is the S-version of coherent rings. Let R=⊕α∈GRαdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$R = mathop oplus limits_{alpha in G} {R_alpha }$$end{document} be a commutative ring with unity graded by an arbitrary commutative monoid G, and S a multiplicatively closed subset of nonzero homogeneous elements of R. We define R to be graded-S-coherent ring if every finitely generated homogeneous ideal of R is S-finitely presented. The purpose of this paper is to give the graded version of several results proved in D. Bennis, M. El Hajoui (2018). We show the nontriviality of our generalization by giving an example of a graded-S-coherent ring which is not S-coherent and as a special case of our study, we give the graded version of the Chase’s characterization of S-coherent rings.
Recently, motivated by Anderson, Dumitrescu’s S-finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S-coherent rings, which is the S-version of coherent rings. Let R=⊕α∈GRαdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$R = mathop oplus limits_{alpha in G} {R_alpha }$$end{document} be a commutative ring with unity graded by an arbitrary commutative monoid G, and S a multiplicatively closed subset of nonzero homogeneous elements of R. We define R to be graded-S-coherent ring if every finitely generated homogeneous ideal of R is S-finitely presented. The purpose of this paper is to give the graded version of several results proved in D. Bennis, M. El Hajoui (2018). We show the nontriviality of our generalization by giving an example of a graded-S-coherent ring which is not S-coherent and as a special case of our study, we give the graded version of the Chase’s characterization of S-coherent rings.
{"title":"Commutative graded-S-coherent rings","authors":"Anass Assarrar, N. Mahdou, Ünsal Tekir, Suat Koç","doi":"10.21136/CMJ.2023.0130-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0130-22","url":null,"abstract":"Recently, motivated by Anderson, Dumitrescu’s S-finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S-coherent rings, which is the S-version of coherent rings. Let R=⊕α∈GRαdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$R = mathop oplus limits_{alpha in G} {R_alpha }$$end{document} be a commutative ring with unity graded by an arbitrary commutative monoid G, and S a multiplicatively closed subset of nonzero homogeneous elements of R. We define R to be graded-S-coherent ring if every finitely generated homogeneous ideal of R is S-finitely presented. The purpose of this paper is to give the graded version of several results proved in D. Bennis, M. El Hajoui (2018). We show the nontriviality of our generalization by giving an example of a graded-S-coherent ring which is not S-coherent and as a special case of our study, we give the graded version of the Chase’s characterization of S-coherent rings.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"553 - 564"},"PeriodicalIF":0.5,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44978792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-31DOI: 10.21136/CMJ.2023.0206-22
Yuchen Ding, G. Zhou
Let l ≽ 2 be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {n_1},{n_2},...,{n_1} leqslant {x^{1/2}}} {{tau _k}(n_1^2 + n_2^2 + ... + n_1^2),} $$end{document} where τk (n) represents the kth divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {p_1},p2,...,{p_1} leqslant x} {{tau _k}({p_1} + {p_2} + ... + {p_l}),} $$end{document} where p1, p2, …, pl are prime variables.
Let l ≽ 2 be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {n_1},{n_2},...,{n_1} leqslant {x^{1/2}}} {{tau _k}(n_1^2 + n_2^2 + ... + n_1^2),} $$end{document} where τk (n) represents the kth divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {p_1},p2,...,{p_1} leqslant x} {{tau _k}({p_1} + {p_2} + ... + {p_l}),} $$end{document} where p1, p2, …, pl are prime variables.
{"title":"Sum of higher divisor function with prime summands","authors":"Yuchen Ding, G. Zhou","doi":"10.21136/CMJ.2023.0206-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0206-22","url":null,"abstract":"Let l ≽ 2 be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {n_1},{n_2},...,{n_1} leqslant {x^{1/2}}} {{tau _k}(n_1^2 + n_2^2 + ... + n_1^2),} $$end{document} where τk (n) represents the kth divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sumlimits_{1 leqslant {p_1},p2,...,{p_1} leqslant x} {{tau _k}({p_1} + {p_2} + ... + {p_l}),} $$end{document} where p1, p2, …, pl are prime variables.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"621 - 631"},"PeriodicalIF":0.5,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.21136/CMJ.2023.0188-21
M. Gil'
We consider the equation dy(t)/dt = (A + B(t))y(t) (t ≽ 0), where A is the generator of an analytic semigroup (eAt)t≽0 on a Banach space χ, B(t) is a variable bounded operator in χ. It is assumed that the commutator K(t) = AB(t) − B(t)A has the following property: there is a linear operator S having a bounded left-inverse operator Sl−1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S_l^{ - 1}$$end{document} such that ∥SeAt∥ is integrable and the operator K(t)Sl−1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Kleft( t right)S_l^{ - 1}$$end{document} is bounded. Under these conditions an exponential stability test is derived. As an example we consider a coupled system of parabolic equations.
我们考虑方程dy（t）/dt=（A+B（t））y（t）（t≽0），其中A是Banach空间χ上分析半群（eAt）t≴0的生成元，B（t）是χ中的可变有界算子。假设交换子K（t）=AB（t）−B（t）A具有以下性质：存在一个线性算子S，它具有一个有界左逆算子Sl−1documentclass[12pt]｛minimal｝usepackage｛amsmath｝ usepackage{wasysym｝ use package{amsfonts｝usapackage｛amssymb｝ usapackage{amsbsy｝usepackage{mathrsfs｝ userpackage{upgeek｝setlength｛oddsidemargin｝｛-69pt｝ begin｛document｝$S_l^｛-1｝$$end｛document｝，使得‖SeAt‖是可积的，并且运算符K（t）Sl−1documentclass[12pt]｛minimal｝usepackage｛amsmath｝use package｛｛wasysym｝ usepackage{amsfonts｝usapackage｛amssymb｝ use package{amsbsy｝usepackage{mathrsfs｝ usapackage{upgek｝setlength｛oddsedmargin｝｛-69pt｝begin｛document｝$Kleft（tright）S_l^｛-1｝$end{document｝是有界的。在这些条件下，导出了指数稳定性检验。作为一个例子，我们考虑一个抛物型方程的耦合系统。
{"title":"Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space","authors":"M. Gil'","doi":"10.21136/CMJ.2023.0188-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0188-21","url":null,"abstract":"We consider the equation dy(t)/dt = (A + B(t))y(t) (t ≽ 0), where A is the generator of an analytic semigroup (eAt)t≽0 on a Banach space χ, B(t) is a variable bounded operator in χ. It is assumed that the commutator K(t) = AB(t) − B(t)A has the following property: there is a linear operator S having a bounded left-inverse operator Sl−1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S_l^{ - 1}$$end{document} such that ∥SeAt∥ is integrable and the operator K(t)Sl−1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Kleft( t right)S_l^{ - 1}$$end{document} is bounded. Under these conditions an exponential stability test is derived. As an example we consider a coupled system of parabolic equations.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"355 - 366"},"PeriodicalIF":0.5,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42755119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-18DOI: 10.21136/CMJ.2023.0411-21
Hanieh Shoar, M. Salimi, A. Tehranian, H. Rasouli, E. Tavasoli
Let R and S be commutative rings with identity, J be an ideal of S, f: R → S be a ring homomorphism, M be an R-module, N be an S-module, and let φ: M → N be an R-homomorphism. The amalgamation of R with S along J with respect to f denoted by R ⨝fJ was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of (R ⨝fJ)-module called the amalgamation of M and N along J with respect to φ, and denoted by M ⨝φJN. We study some homological properties of the (R ⨝fJ)-module M ⨝φJN. Among other results, we investigate projectivity, flatness, injectivity, Cohen-Macaulayness, and prime property of the (R ⨝fJ)-module M ⨝φJN in connection to their corresponding properties of the R-modules M and JN.
设R和S是具有恒等的交换环，J是S的理想，f: R→S是环同态，M是R模，N是S模，φ: M→N是R同态。M. D 'Anna et al.(2010)引入了R与S以及J相对于f的合并，用R⨝fJ表示。最近，R. El Khalfaoui等人(2021)引入了一种特殊的(R⨝fJ)模，称为M和N沿J对φ的合并，用M⨝φ jn表示。研究了(R⨝fJ)-模M⨝φJN的一些同调性质。在其他结果中，我们研究了(R⨝fJ)-模M⨝φJN的投影性、平坦性、注入性、Cohen-Macaulayness和素数性质，并与它们对应的R-模M和JN的性质联系起来。
{"title":"Some homological properties of amalgamated modules along an ideal","authors":"Hanieh Shoar, M. Salimi, A. Tehranian, H. Rasouli, E. Tavasoli","doi":"10.21136/CMJ.2023.0411-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0411-21","url":null,"abstract":"Let R and S be commutative rings with identity, J be an ideal of S, f: R → S be a ring homomorphism, M be an R-module, N be an S-module, and let φ: M → N be an R-homomorphism. The amalgamation of R with S along J with respect to f denoted by R ⨝fJ was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of (R ⨝fJ)-module called the amalgamation of M and N along J with respect to φ, and denoted by M ⨝φJN. We study some homological properties of the (R ⨝fJ)-module M ⨝φJN. Among other results, we investigate projectivity, flatness, injectivity, Cohen-Macaulayness, and prime property of the (R ⨝fJ)-module M ⨝φJN in connection to their corresponding properties of the R-modules M and JN.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"475 - 486"},"PeriodicalIF":0.5,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48868842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-18DOI: 10.21136/CMJ.2023.0127-22
Jian He, Jing He, Panyue Zhou
The aim of this article is to study the relative Auslander bijection in n-exangulated categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
{"title":"Relative Auslander bijection in n-exangulated categories","authors":"Jian He, Jing He, Panyue Zhou","doi":"10.21136/CMJ.2023.0127-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0127-22","url":null,"abstract":"The aim of this article is to study the relative Auslander bijection in n-exangulated categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"525 - 552"},"PeriodicalIF":0.5,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43662055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-05DOI: 10.21136/CMJ.2023.0282-21
Junquan Qin, Xiaoyan Yang
The goal of the article is to develop a theory dual to that of support in the derived category D(R). This is done by introducing ‘big’ and ‘small’ cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between ‘big’ and ‘small’ cosupport and give some comparisons of support and cosupport. Finally, we investigate the dual notion of associated primes.
{"title":"Another version of cosupport in D(R)","authors":"Junquan Qin, Xiaoyan Yang","doi":"10.21136/CMJ.2023.0282-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0282-21","url":null,"abstract":"The goal of the article is to develop a theory dual to that of support in the derived category D(R). This is done by introducing ‘big’ and ‘small’ cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between ‘big’ and ‘small’ cosupport and give some comparisons of support and cosupport. Finally, we investigate the dual notion of associated primes.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"431 - 452"},"PeriodicalIF":0.5,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43279098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-03DOI: 10.21136/CMJ.2023.0259-21
Emel Aslankarayiğit Uğurlu, E. M. Bouba, Ünsal Tekir, Suat Koç
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R. The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ ab ∈ Q for some a, b ∈ R, then a2 ∈ Q or b∈Qdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$b in sqrt Q $$end{document}. Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.
我们在交换环中引入弱强拟初等（简称wsq初等）理想。设R是一个具有非零恒等式的交换环，Q是R的适当理想。适当理想Q被称为弱强拟初理想，如果对于某个a，b∈R，则a2∈Q或b∈Qdocumentclass[12pt]｛minimum｝usepackage｛amsmath｝userpackage｛wasysym｝use package｛amsfonts｝usapackage｛amssymb｝ usepackage{amsbsy｝ use package{mathrsfs｝ usapackage{upgeek｝setlength｛doddsidemargin｝｛-69pt｝begin｛document｝$binsqrt Q$end｛document｝。给出了wsq初理想的许多例子和性质。此外，我们还刻画了非局部Noetherian-von Neumann正则环、域、每个适当理想是wsq初等的非局部环，以及每个适当理想都是wsq初级的零维环。最后，我们研究了wsq初理想的有限并集。
{"title":"On wsq-primary ideals","authors":"Emel Aslankarayiğit Uğurlu, E. M. Bouba, Ünsal Tekir, Suat Koç","doi":"10.21136/CMJ.2023.0259-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0259-21","url":null,"abstract":"We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R. The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ ab ∈ Q for some a, b ∈ R, then a2 ∈ Q or b∈Qdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$b in sqrt Q $$end{document}. Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"415 - 429"},"PeriodicalIF":0.5,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43483450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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