2018-10-22T17:40:33Z
http://jart.guilan.ac.ir/?_action=export&rf=summon&issue=17
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
Line graphs associated to the maximal graph
A.
Sharma
A.
Gaur
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.
Maximal graph
line graph
eulerian graph
comaximal graph
2015
06
01
1
11
http://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
Strongly cotop modules
H.
Ansari-Toroghy
S.S.
Pourmortazavi
S.
Keyvani
In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.
Second submodule
strongly cotop module
Zariski topology
spectral space
2015
06
01
13
29
http://jart.guilan.ac.ir/article_1210_4cce280ab88cc7218f63973c940d1f25.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
On the fitting ideals of a comultiplication module
S.
Karimzadeh
S.
Hadjirezaei
Let $R$ be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.
Fitting ideals
comultiplication module
simple module
2015
06
01
31
39
http://jart.guilan.ac.ir/article_1211_33e4f18032e4525d4779c336be03ffab.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
F-regularity relative to modules
F.
Dorostkar
R.
khosravi
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 .
Tight closure
$F-$regular
and weakly $F-$regular relative to a module
2015
06
01
41
50
http://jart.guilan.ac.ir/article_1212_1707024d6a7b82e8d1892f7dbb86f9ff.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
A note on maximal non-prime ideals
S.
Visweswaran
A.
Parmar
The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. 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 $ Isubseteq A$ and $Ineq A$ 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 $R$.
Maximal non-prime ideal
maximal non-maximal ideal
maximal non-primary ideal
maximal non-irreducible ideal
2015
06
01
51
61
http://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2015
3
1
Some numerical results on two classes of finite groups
M.
Hashemi
M.
Polkouei
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$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, $m,ngeq 2$ and $g.c.d(s,l)=1$.
Nilpotent groups
$n^{th}$-commutativity degree
$n$-abelian groups
2015
06
01
63
72
http://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf