@Article{Sharma2015,
author="Sharma, A.
and Gaur, A.",
title="Line graphs associated to the maximal graph",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="1-11",
abstract="Let $R$ 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.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1209.html"
}
@Article{Ansari-Toroghy2015,
author="Ansari-Toroghy, H.
and Pourmortazavi, S.S.
and Keyvani, S.",
title="Strongly cotop modules",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="13-29",
abstract="In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1210.html"
}
@Article{Karimzadeh2015,
author="Karimzadeh, S.
and Hadjirezaei, S.",
title="On the fitting ideals of a comultiplication module",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="31-39",
abstract="Let $R$ be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1211.html"
}
@Article{Dorostkar2015,
author="Dorostkar, F.
and khosravi, R.",
title="F-regularity relative to modules",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="41-50",
abstract="In 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 .",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1212.html"
}
@Article{Visweswaran2015,
author="Visweswaran, S.
and Parmar, A.",
title="A note on maximal non-prime ideals",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="51-61",
abstract="The 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 $R$.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1213.html"
}
@Article{Hashemi2015,
author="Hashemi, M.
and Polkouei, M.",
title="Some numerical results on two classes of finite groups",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="1",
pages="63-72",
abstract="In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=\langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]\rangle $$$$K(s,l)=\langle a,b|ab^s=b^la,~ba^s=a^lb\rangle;$$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 $g.c.d(s,l)=1$.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1214.html"
}