{"title":"Category of $n$-FCP-gr-projective modules with respect to special copresented graded modules","authors":"M. Amini, D. Bennis, Soumia Mamdouhi","doi":"10.24330/ieja.1068810","DOIUrl":"https://doi.org/10.24330/ieja.1068810","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46121419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $mathcal{J}_{field}$ be the Jordan triple system of all $p times q$ ($pneq q$; $p,q >1)$ rectangular matrices over a field $field$ of characteristic 0 with the triple product ${x,y,z}= x y^t z+ z y^t x $, where $y^t$ is the transpose of $y$. We study the universal associative envelope $mathcal{U}(mathcal{J}_{field})$ of $mathcal{J}_{field}$ and show that $mathcal{U}(mathcal{J}_{field}) cong M_{p+q times p+q}(field)$, where $M_{p+qtimes p+q} (field)$ is the ordinary associative algebra of all $(p+q) times (p+q)$ matrices over $field$. It follows that there exists only one nontrivial irreducible representation of $mathcal{J}_{field}$. The center of $mathcal{U}(mathcal{J}_{field})$ is deduced.
设$mathcal{J}_{field}$为所有的Jordan三重系统$p times q$ ($pneq q$;$p,q >1)$特征为0的域$field$上的矩形矩阵与三重积${x,y,z}= x y^t z+ z y^t x $，其中$y^t$是$y$的转置。我们研究了$mathcal{J}_{field}$的普遍关联包络$mathcal{U}(mathcal{J}_{field})$，并证明了$mathcal{U}(mathcal{J}_{field}) cong M_{p+q times p+q}(field)$，其中$M_{p+qtimes p+q} (field)$是$field$上所有$(p+q) times (p+q)$矩阵的普通关联代数。由此可见，$mathcal{J}_{field}$只存在一个非平凡的不可约表示。推导出$mathcal{U}(mathcal{J}_{field})$的中心。
{"title":"On the irreducible representations of the Jordan triple system of $p times q$ matrices","authors":"Hader A. Elgendy","doi":"10.24330/ieja.1226320","DOIUrl":"https://doi.org/10.24330/ieja.1226320","url":null,"abstract":"Let $mathcal{J}_{field}$ be the Jordan triple system of all $p times q$ ($pneq q$; $p,q >1)$ rectangular matrices over a field $field$ of characteristic 0 with the triple product ${x,y,z}= x y^t z+ z y^t x $, where $y^t$ is the transpose of $y$. We study the universal associative envelope $mathcal{U}(mathcal{J}_{field})$ of $mathcal{J}_{field}$ and show that $mathcal{U}(mathcal{J}_{field}) cong M_{p+q times p+q}(field)$, where $M_{p+qtimes p+q} (field)$ is the ordinary associative algebra of all $(p+q) times (p+q)$ matrices over $field$. It follows that there exists only one nontrivial irreducible representation of $mathcal{J}_{field}$. The center of $mathcal{U}(mathcal{J}_{field})$ is deduced.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42996624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] and [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity and vertex decomposability of simple graphs. In this paper, we give negative answers to the questions by providing two counterexamples.
{"title":"On vertex decomposability and regularity of graphs","authors":"A. Mafi, Dler Naderi, Parasto Soufivand","doi":"10.24330/ieja.1217285","DOIUrl":"https://doi.org/10.24330/ieja.1217285","url":null,"abstract":"There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] and [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity and vertex decomposability of simple graphs. In this paper, we give negative answers to the questions by providing two counterexamples.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49554967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We introduce some new lattices of classes of modules with respect to appropriate preradicals. We introduce some concepts associated with these lattices, such as the σ -semiartinian rings, the σ -retractable modules, the σ - V -rings, the σ -max rings. We continue to study σ -torsion theories, σ -open classes, σ -stable classes. We prove some theorems that extend some known results. Our results fall into well known situations when the preradical σ is chosen as the identity preradical.
{"title":"On lattices associated to rings with respect to a preradical","authors":"Erwin Cerda-León, H. Rincón-Mejía","doi":"10.24330/ieja.1058385","DOIUrl":"https://doi.org/10.24330/ieja.1058385","url":null,"abstract":". We introduce some new lattices of classes of modules with respect to appropriate preradicals. We introduce some concepts associated with these lattices, such as the σ -semiartinian rings, the σ -retractable modules, the σ - V -rings, the σ -max rings. We continue to study σ -torsion theories, σ -open classes, σ -stable classes. We prove some theorems that extend some known results. Our results fall into well known situations when the preradical σ is chosen as the identity preradical.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41465858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let ∆ be a simplicial complex, I∆ its Stanley-Reisner ideal and R = K[∆] its Stanley-Reisner ring over a field K. In 2018, the author introduced the squarefree zero-divisor graph of R, denoted by Γsf(R), and proved that if ∆ and ∆′ are two simplicial complexes, then the graphs Γsf(K[∆]) and Γsf(K[∆ ′]) are isomorphic if and only if the rings K[∆] and K[∆′] are isomorphic. Here we derive some algebraic properties of R using combinatorial properties of Γsf(R). In particular, we state combinatorial conditions on Γsf(R) which are necessary or sufficient for R to be Cohen-Macaulay. Moreover, we investigate when Γsf(R) is in some well-known classes of graphs and show that in these cases, I∆ has a linear resolution or is componentwise linear. Also we study the diameter and girth of Γsf(R) and their algebraic interpretations. Mathematics Subject Classification (2020): 13F55, 13C70, 05C25, 05E40
{"title":"Deriving Some Properties of Stanley-Reisner Rings from Their Squarefree Zero-Divisor Graphs","authors":"A. Nikseresht","doi":"10.24330/ieja.1058421","DOIUrl":"https://doi.org/10.24330/ieja.1058421","url":null,"abstract":"Let ∆ be a simplicial complex, I∆ its Stanley-Reisner ideal and R = K[∆] its Stanley-Reisner ring over a field K. In 2018, the author introduced the squarefree zero-divisor graph of R, denoted by Γsf(R), and proved that if ∆ and ∆′ are two simplicial complexes, then the graphs Γsf(K[∆]) and Γsf(K[∆ ′]) are isomorphic if and only if the rings K[∆] and K[∆′] are isomorphic. Here we derive some algebraic properties of R using combinatorial properties of Γsf(R). In particular, we state combinatorial conditions on Γsf(R) which are necessary or sufficient for R to be Cohen-Macaulay. Moreover, we investigate when Γsf(R) is in some well-known classes of graphs and show that in these cases, I∆ has a linear resolution or is componentwise linear. Also we study the diameter and girth of Γsf(R) and their algebraic interpretations. Mathematics Subject Classification (2020): 13F55, 13C70, 05C25, 05E40","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48386060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Bell polynomials associated to Vasyunin cotangent sums","authors":"Samir Belhadj, M. Goubi","doi":"10.24330/ieja.1058435","DOIUrl":"https://doi.org/10.24330/ieja.1058435","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49615562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$pi$-BAER $ast$-RINGS","authors":"Ali Shahidikia, H. Javadi, A. Moussavi","doi":"10.24330/IEJA.969915","DOIUrl":"https://doi.org/10.24330/IEJA.969915","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43799801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S. Tchamna, A study of linked star operations, to appear in Bull. Korean Math. Soc., Definition 3.1]. We establish some results on star operations, and we study P?ME in pullback diagrams of type . We show that, for a maximal ideal m of R, the extension R[m] ⊆ S is Manis if and only if R[X][mR[X]] ⊆ S[X] is a Manis extension. Mathematics Subject Classification (2020): 13A15, 13A18, 13B02
{"title":"SOME PROPERTIES OF STAR OPERATIONS ON RING EXTENSIONS","authors":"Lokendra Paudel, S. Tchamna","doi":"10.24330/IEJA.969592","DOIUrl":"https://doi.org/10.24330/IEJA.969592","url":null,"abstract":"Let ? be a star operation on a ring extension R ⊆ S. A ring extension R ⊆ S is called Prüfer star-multiplication extension (P?ME) if (R[m],m[m]) is a Manis pair in S for every ?-maximal ideal m of R [L. Paudel and S. Tchamna, A study of linked star operations, to appear in Bull. Korean Math. Soc., Definition 3.1]. We establish some results on star operations, and we study P?ME in pullback diagrams of type . We show that, for a maximal ideal m of R, the extension R[m] ⊆ S is Manis if and only if R[X][mR[X]] ⊆ S[X] is a Manis extension. Mathematics Subject Classification (2020): 13A15, 13A18, 13B02","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46662291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS","authors":"Huihui Zheng, Yuan-yuan Chen, Liangyun Zhang","doi":"10.24330/IEJA.969590","DOIUrl":"https://doi.org/10.24330/IEJA.969590","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46913033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS","authors":"G. Călugăreanu, A. Chekhlov","doi":"10.24330/IEJA.969907","DOIUrl":"https://doi.org/10.24330/IEJA.969907","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46603243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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