Pub Date : 2022-01-01DOI: 10.59277/mrar.2023.25.75.1.133
Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi
"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases."
设R是一个noether环，I是R的一个理想，设M是一个有限生成的R模，cd(I,M) = t≥0，并设L是M的最大子模，使得cd(I,L) < cd(I,M)。可以看出，在以下情况下，AnnR Ht I (M) = AnnRM/L:(I) dimM/IM≤1。(ii) dimR/I≤1。(iii)当I≥2时，r模Hi I (M)为Artinian。(iv)当I≥2时，R模Hi I (R)为Artinian。(v) cd(I,M)≤1。(vi) cd(I,R)≤1。(vii) r模hti (M)是Artinian和I- finite。这些断言肯定地回答了Atazadeh等人在[2]中在某些特殊情况下提出的问题。”
{"title":"\"COFINITENESS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES\"","authors":"Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi","doi":"10.59277/mrar.2023.25.75.1.133","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.133","url":null,"abstract":"\"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"37 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78074067","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 : 2022-01-01DOI: 10.59277/mrar.2023.25.75.1.73
D. Andrica, George C. Ţurcaş
"We present two Diophantine equations that arise from some new results in the theory of partitions with equal sums. We link these to the problem of finding rational points on some hyperelliptic curves and we solve the latter, assisted by computer algebra packages, using a p-adic method pioneered by Chabauty and Coleman."
{"title":"\"HYPERELLIPTIC DIOPHANTINE EQUATIONS FROM THE STUDY OF PARTITIONS\"","authors":"D. Andrica, George C. Ţurcaş","doi":"10.59277/mrar.2023.25.75.1.73","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.73","url":null,"abstract":"\"We present two Diophantine equations that arise from some new results in the theory of partitions with equal sums. We link these to the problem of finding rational points on some hyperelliptic curves and we solve the latter, assisted by computer algebra packages, using a p-adic method pioneered by Chabauty and Coleman.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"29 4","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72431256","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 : 2022-01-01DOI: 10.59277/mrar.2023.25.75.1.47
L. Gallardo, O. Rahavandrainy
"Perfect polynomials are a natural analogue (in the ring Fp[x]) of multiperfect numbers (in the ring of integers). The latter numbers are classical objects that are poorly understood, since only their definition is simple. We describe, by elementary methods, the most basic objects in the polynomial case of the general problem. We display, for every prime number p ̸≡ 1mod 12 (resp. p ̸≡ 1mod 24) many new even non-splitting perfect (resp. unitary perfect) polynomials over Fp. Moreover, for any prime number p ̸≡ 1mod 24, new bi-unitary perfect polynomials are also given. These examples substantially improve our knowledge about these kinds of polynomials."
{"title":"EXISTENCE OF EVEN PERFECT POLYNOMIALS","authors":"L. Gallardo, O. Rahavandrainy","doi":"10.59277/mrar.2023.25.75.1.47","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.47","url":null,"abstract":"\"Perfect polynomials are a natural analogue (in the ring Fp[x]) of multiperfect numbers (in the ring of integers). The latter numbers are classical objects that are poorly understood, since only their definition is simple. We describe, by elementary methods, the most basic objects in the polynomial case of the general problem. We display, for every prime number p ̸≡ 1mod 12 (resp. p ̸≡ 1mod 24) many new even non-splitting perfect (resp. unitary perfect) polynomials over Fp. Moreover, for any prime number p ̸≡ 1mod 24, new bi-unitary perfect polynomials are also given. These examples substantially improve our knowledge about these kinds of polynomials.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"147 6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83109906","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 : 2022-01-01DOI: 10.59277/mrar.2023.25.75.1.103
Esmaeil Rostami, S. Hedayat
"In this paper, the concept of clean ring is generalized to modules. We call a free R-module, Rn, clean, whenever every element of Rn can be written as the sum of a unimodular and an idempotent row. We show that when R is Noetherian, the R-module Rn is clean if and only if R can be expressed as a finite direct product of indecomposable rings Ri, say R = Lt i=1 Ri, such that each Ri has at most 2n − 1 maximal ideals. We also give a new characterization of clean rings."
{"title":"\"ON CLEAN FREE MODULES AND A CHARACTERIZATION OF CLEAN RINGS\"","authors":"Esmaeil Rostami, S. Hedayat","doi":"10.59277/mrar.2023.25.75.1.103","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.1.103","url":null,"abstract":"\"In this paper, the concept of clean ring is generalized to modules. We call a free R-module, Rn, clean, whenever every element of Rn can be written as the sum of a unimodular and an idempotent row. We show that when R is Noetherian, the R-module Rn is clean if and only if R can be expressed as a finite direct product of indecomposable rings Ri, say R = Lt i=1 Ri, such that each Ri has at most 2n − 1 maximal ideals. We also give a new characterization of clean rings.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"44 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91339157","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 : 2019-12-07DOI: 10.59277/mrar.2023.25.75.2.287
C. Beli
If V is a vector space over some field F, then we have the well known exact sequence 0 → Λ2(V ) → T2(V ) → S2(V ) → 0, where the first map is given by x∧y → x⊗y−y⊗x and the second by x⊗y 7→ xy. The obvious generalization, an exact sequence, 0 → Λk(V ) → T
{"title":"ON THE KERNEL OF THE PROJECTION MAP T(V ) → S(V )","authors":"C. Beli","doi":"10.59277/mrar.2023.25.75.2.287","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.287","url":null,"abstract":"If V is a vector space over some field F, then we have the well known exact sequence 0 → Λ2(V ) → T2(V ) → S2(V ) → 0, where the first map is given by x∧y → x⊗y−y⊗x and the second by x⊗y 7→ xy. The obvious generalization, an exact sequence, 0 → Λk(V ) → T","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"3 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2019-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84511849","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 : 2019-02-11DOI: 10.59277/mrar.2023.25.75.2.301
A. Shamsaki, P. Niroomand
It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra L of dimension n is equal to 1 2 (n − 1)(n − 2) + 1 − s(L) for some s(L) ≥ 0. The structure of all nilpotent Lie algebras has been given for s(L) ≤ 4 in several
{"title":"CHARACTERIZATION OF FINITE DIMENSIONAL NILPOTENT LIE ALGEBRAS BY THE DIMENSION OF THEIR SCHUR MULTIPLIERS, s(L) = 5","authors":"A. Shamsaki, P. Niroomand","doi":"10.59277/mrar.2023.25.75.2.301","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.301","url":null,"abstract":"It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra L of dimension n is equal to 1 2 (n − 1)(n − 2) + 1 − s(L) for some s(L) ≥ 0. The structure of all nilpotent Lie algebras has been given for s(L) ≤ 4 in several","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2019-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80017737","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 : 2018-10-24DOI: 10.59277/mrar.2023.25.75.2.349
A. Vahidi, M. Aghapournahr, E. M. Renani
Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a nite R-module, and n a non-negative integer. In this paper, for an arbitrary R-module X which is not necessarily nite, we prove the following results: (i) fn a (M;X) = i
设R是一个非零单位元的交换诺瑟环，a是R的理想，M是一个非负模，n是一个非负整数。对于任意r模X，我们证明了以下结果:(i) fn a (M;X) = i
{"title":"FINITENESS DIMENSIONS AND COFINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES","authors":"A. Vahidi, M. Aghapournahr, E. M. Renani","doi":"10.59277/mrar.2023.25.75.2.349","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.349","url":null,"abstract":"Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a nite R-module, and n a non-negative integer. In this paper, for an arbitrary R-module X which is not necessarily nite, we prove the following results: (i) fn a (M;X) = i","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"59 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81171131","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 : 2018-03-08DOI: 10.59277/mrar.2023.25.75.2.263
J. Kratica, A. Savi'c, Zoran Lj. Maksimovi'c
The recently introduced {k}-packing function problem is considered in this paper. Relationship between cases when k = 1, k ≥ 2 and linear programming relaxation are introduced with sufficient conditions for optimality. For arbitrary simple connected graph
{"title":"SOME PROPERTIES OF {k}-PACKING FUNCTION PROBLEM IN GRAPHS","authors":"J. Kratica, A. Savi'c, Zoran Lj. Maksimovi'c","doi":"10.59277/mrar.2023.25.75.2.263","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.263","url":null,"abstract":"The recently introduced {k}-packing function problem is considered in this paper. Relationship between cases when k = 1, k ≥ 2 and linear programming relaxation are introduced with sufficient conditions for optimality. For arbitrary simple connected graph","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"99 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2018-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75977192","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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