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International Electronic Journal of Algebra最新文献

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SOME REMARKS ON THE ORDER SUPERGRAPH OF THE POWER GRAPH OF A FINITE GROUP 有限群幂图的阶超图的若干注释
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586838
A. Hamzeh, A. Ashrafi
{"title":"SOME REMARKS ON THE ORDER SUPERGRAPH OF THE POWER GRAPH OF A FINITE GROUP","authors":"A. Hamzeh, A. Ashrafi","doi":"10.24330/IEJA.586838","DOIUrl":"https://doi.org/10.24330/IEJA.586838","url":null,"abstract":"Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x)|o(y) or o(y)|o(x). In an earlier paper, the main properties of this graph was obtained. The aim of this paper is to investigate the Hamiltonianity, Eulerianness and 2-connectedness of this graph.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47833113","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}
引用次数: 3
INJECTIVE MODULES WITH RESPECT TO MODULES OF PROJECTIVE DIMENSION AT MOST ONE 关于投影维数至多为1的模的内射模
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586945
S. Bouchiba, M. El-Arabi
{"title":"INJECTIVE MODULES WITH RESPECT TO MODULES OF PROJECTIVE DIMENSION AT MOST ONE","authors":"S. Bouchiba, M. El-Arabi","doi":"10.24330/IEJA.586945","DOIUrl":"https://doi.org/10.24330/IEJA.586945","url":null,"abstract":"Several authors have been interested in cotorsion theories. Among these theories we figure the pairs $(mathcal P_n,mathcal P_n^{perp})$, where $mathcal P_n$ designates the set of modules of projective dimension at most a given integer $ngeq 1$  over a ring $R$. In this paper, we shall focus on homological properties of the class $mathcal P_1^{perp}$ that we term the class of $mathcal P_1$-injective modules. Numerous nice characterizations of rings as well as of their homological dimensions arise from this study. In particular, it is shown that a ring $R$ is left hereditary if and only if any $mathcal P_1$-injective module is injective and that $R$ is  left semi-hereditary if and only if any $mathcal P_1$-injective module is FP-injective. Moreover, we prove that the global dimensions of $R$ might be computed in terms of $mathcal P_1$-injective modules, namely the formula for the global dimension and the weak global dimension turn out to be as follows $$wdim(R)=sup {fd_R(M): Mmbox { is a }mathcal P_1mbox {-injective left } Rmbox {-module} }$$ and $$gdim(R)=sup {pd_R(M):M mbox { is a }mathcal P_1mbox {-injective left }Rmbox {-module}}.$$ We close the paper by proving that, given a Matlis domain $R$ and an $R$-module $Minmathcal P_1$, $Hom_R(M,N)$ is $mathcal P_1$-injective for each $mathcal P_1$-injective module $N$ if and only if $M$ is strongly flat.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43289411","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}
引用次数: 0
ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS 关于关联素数理想和平方主BOREL理想的幂深度
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.587081
J. Herzog, B. Lajmiri, F. Rahmati
{"title":"ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS","authors":"J. Herzog, B. Lajmiri, F. Rahmati","doi":"10.24330/IEJA.587081","DOIUrl":"https://doi.org/10.24330/IEJA.587081","url":null,"abstract":"We study algebraic properties of powers of squarefree principal Borel ideals I, and show that astab(I) = dstab(I). Furthermore, the behaviour of the depth function depth S/I^k is considered.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48547085","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}
引用次数: 4
ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS 交换环上的莱维特路径代数
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.587053
P. Kanwar, M. Khatkar, Rajneesh Sharma
{"title":"ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS","authors":"P. Kanwar, M. Khatkar, Rajneesh Sharma","doi":"10.24330/IEJA.587053","DOIUrl":"https://doi.org/10.24330/IEJA.587053","url":null,"abstract":"In this article, basic ideals in a Leavitt path algebra over a com- mutative unital ring are studied. It is shown that for a nite acyclic graph E and a commutative unital ring R, the Leavitt path algebra LR(E) is a direct sum of minimal basic ideals and that for a commutative ring R and a graph E satisfying Condition (L), the Leavitt path algebra LR(E) has no non-zero nilpotent basic ideals. Uniqueness theorems for Leavitt path algebras over commutative unital rings are also discussed.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42714537","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}
引用次数: 2
A GENERALIZATION OF SIMPLE-INJECTIVE RINGS 单射环的一个推广
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586952
Zhu Zhanmin
{"title":"A GENERALIZATION OF SIMPLE-INJECTIVE RINGS","authors":"Zhu Zhanmin","doi":"10.24330/IEJA.586952","DOIUrl":"https://doi.org/10.24330/IEJA.586952","url":null,"abstract":"A ring R is called right 2-simple J-injective if, for every 2-generated right ideal I < J(R), every R-linear map from I to R with simple image ex tends to R. The class of right 2-simple J-injective rings is broader than that of right 2-simple injective rings and right simple J-injective rings. Right 2-simple J-injective right Kasch rings are studied, several conditions under which right 2-simple J-injective rings are QF-rings are given.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47842135","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}
引用次数: 0
ON A SPECIAL PRESENTATION OF MATRIX ALGEBRAS 关于矩阵代数的一个特殊表示
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.662946
G. Agnarsson, S. Mendelson
{"title":"ON A SPECIAL PRESENTATION OF MATRIX ALGEBRAS","authors":"G. Agnarsson, S. Mendelson","doi":"10.24330/IEJA.662946","DOIUrl":"https://doi.org/10.24330/IEJA.662946","url":null,"abstract":"Recognizing when a ring is a complete matrix ring is of significant importance in algebra. It is well-known folklore that a ring $R$ is a complete $ntimes n$ matrix ring, so $Rcong M_{n}(S)$ for some ring $S$, if and only if it contains a set of $ntimes n$ matrix units ${e_{ij}}_{i,j=1}^n$. A more recent and less known result states that a ring $R$ is a complete $(m+n)times(m+n)$ matrix ring if and only if, $R$ contains three elements, $a$, $b$, and $f$, satisfying the two relations $af^m+f^nb=1$ and $f^{m+n}=0$. In many instances the two elements $a$ and $b$ can be replaced by appropriate powers $a^i$ and $a^j$ of a single element $a$ respectively. In general very little is known about the structure of the ring $S$. In this article we study in depth the case $m=n=1$ when $Rcong M_2(S)$. More specifically we study the universal algebra over a commutative ring $A$ with elements $x$ and $y$ that satisfy the relations $x^iy+yx^j=1$ and $y^2=0$. We describe completely the structure of these $A$-algebras and their underlying rings when $gcd(i,j)=1$. Finally we obtain results that fully determine when there are surjections onto $M_2({mathbb F})$ when ${mathbb F}$ is a base field ${mathbb Q}$ or ${mathbb Z}_p$ for a prime number $p$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44373959","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}
引用次数: 0
ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS 关于两个子代数之和的有限维代数
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.587018
M. Kosan, J. Žemlička
{"title":"ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS","authors":"M. Kosan, J. Žemlička","doi":"10.24330/IEJA.587018","DOIUrl":"https://doi.org/10.24330/IEJA.587018","url":null,"abstract":"In this paper, we give a general method of the construction of a 3-dimensional associative algebra R over an arbitrary field F that is a sum of two subalgebras R_1 and R_2 (i.e. R = R_1 + R_2).","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42706762","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}
引用次数: 1
ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS 由一对理想定义的上局部上同模的湮灭子
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586962
S. Karimi, S. Payrovi
{"title":"ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS","authors":"S. Karimi, S. Payrovi","doi":"10.24330/IEJA.586962","DOIUrl":"https://doi.org/10.24330/IEJA.586962","url":null,"abstract":"Let  $R$ be a commutative Noetherian ring,  $I, J$ two proper ideals of $R$ and let $M$ be a non-zero finitely generated  $R$-module with $c={rm cd}(I,J,M)$. In this paper, we first  introduce $T_R(I,J,M)$ as the largest submodule of $M$ with the property that ${rm cd}(I,J,T_R(I,J,M))<c$ and we describe it in terms of the reduced primary decomposition of zero submodule of $M$. It is shown that  ${rm Ann}_R(H_{I,J}^d(M))={rm Ann}_R(M/{T_R(I,J,M)})$ and ${rm Ann}_R(H_{I}^d(M))={rm Ann}_R(H_{I,J}^d(M))$, whenever $R$ is a  local ring, $M$ has dimension $d$ with $H_{I,J}^d(M)neq0$ and $J^tMsubseteq T_R(I,M)$ for some positive integer $t$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46801677","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}
引用次数: 3
ON alpha-ALMOST QUASI ARTINIAN MODULES 关于 -几乎拟人工模
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586913
M. Davoudian
{"title":"ON alpha-ALMOST QUASI ARTINIAN MODULES","authors":"M. Davoudian","doi":"10.24330/IEJA.586913","DOIUrl":"https://doi.org/10.24330/IEJA.586913","url":null,"abstract":"In this article we introduce and study the concepts of alpha-almost quasi Artinian and  alpha -quasi Krull modules. Using these concepts we extend some of the basic results of  alpha -almost Artinian and  alpha -Krull modules to  alpha - almost quasi Artinian and  alpha -quasi Krull modules. We observe that if M is an alpha -quasi Krull module then the quasi Krull dimension of M is either  alpha  or  alpha +1.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949459","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}
引用次数: 0
ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS 关于回拉环上的拟乘法模
IF 0.6
International Electronic Journal of Algebra Pub Date : 2019-07-11 DOI: 10.24330/IEJA.586980
S. E. Atani, F. Saraei
{"title":"ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS","authors":"S. E. Atani, F. Saraei","doi":"10.24330/IEJA.586980","DOIUrl":"https://doi.org/10.24330/IEJA.586980","url":null,"abstract":"We classify all indecomposable quasi comultiplication modules over pullback of two Dedekind domains. We extend the de nitions and the results of comultiplication modules over pullback rings to a more general quasi comultiplication modules case.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48460239","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}
引用次数: 0
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