University of GuilanJournal of Algebra and Related Topics2345-39313120150601Line graphs associated to the maximal graph1111209ENA.SharmaUniversity of DelhiA.GaurUniversity of DelhiJournal Article20150217Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $\Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphical properties of the line graph associated to $\Gamma(R)$, denoted by $(\Gamma(R))$ such that diameter, completeness, and Eulerian property. A complete characterization of rings is given for which $diam(L(\Gamma(R)))= diam(\Gamma(R))$ or $diam(L(\Gamma(R)))< diam(\Gamma(R))$ or $diam((\Gamma(R)))> diam(\Gamma(R))$. We have shown that the complement of the maximal graph $G(R)$, i.e., the comaximal graph is a Euler graph if and only if $R$ has odd cardinality. We also discuss the Eulerian property of the line graph associated to the comaximal graph.https://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39313120150601Strongly cotop modules13291210ENH.Ansari-ToroghyUniversity of GuilanS.S.PourmortazaviUniversity of GuilanS.KeyvaniIslamic Azad UniversityJournal Article20150112In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.https://jart.guilan.ac.ir/article_1210_4cce280ab88cc7218f63973c940d1f25.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39313120150601On the fitting ideals of a comultiplication module31391211ENS.KarimzadehVali-e-Asr University of Rafsanjan0000-0002-8395-2626S.HadjirezaeiVali-e-Asr University of Rafsanjan0000-0002-8994-5523Journal Article20150111Let $R$ be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.https://jart.guilan.ac.ir/article_1211_33e4f18032e4525d4779c336be03ffab.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39313120150601F-regularity relative to modules41501212ENF.DorostkarUniversity of GuilanR.KhosraviUniversity of GuilanJournal Article20151009In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .https://jart.guilan.ac.ir/article_1212_1707024d6a7b82e8d1892f7dbb86f9ff.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39313120150601A note on maximal non-prime ideals51611213ENS.VisweswaranSaurashtra UniversityA.ParmarSaurashtra UniversityJournal Article20150612The rings considered in this article are commutative with identity $1\neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $I\neq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ I\subseteq A$ and $I\neq A$ is a prime ideal. That is, among all the proper ideals of $R$, $I$ is maximal with respect to the property of being not a prime ideal. The concept of maximal non-maximal ideal and maximal non-primary ideal of a ring can be similarly defined. The aim of this article is to characterize ideals $I$ of a ring $R$ such that $I$ is a maximal non-prime (respectively, a maximal non maximal, a maximal non-primary) ideal of $R$.https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39313120150601Some numerical results on two classes of finite groups63721214ENM.HashemiUniversity of GuilanM.PolkoueiUniversity of GuilanJournal Article20150317In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;<br />$$G_{m}=\langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]\rangle $$<br />$$K(s,l)=\langle a,b|ab^s=b^la,~ba^s=a^lb\rangle;$$<br />and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,n\geq 2$ and $g.c.d(s,l)=1$.https://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf