University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
Line graphs associated to the maximal graph
1
11
EN
A.
Sharma
University of Delhi
anirudh.maths@gmail.com
A.
Gaur
University of Delhi
gaursatul@gmail.com
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
http://jart.guilan.ac.ir/article_1209.html
http://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
Strongly cotop modules
13
29
EN
H.
Ansari-Toroghy
University of Guilan
ansari@guilan.ac.ir
S.S.
Pourmortazavi
University of Guilan
mortazavi@phd.guilan.ac.ir
S.
Keyvani
Islamic Azad University
keivani@bandaranzaliiau.ac.ir
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
http://jart.guilan.ac.ir/article_1210.html
http://jart.guilan.ac.ir/article_1210_4cce280ab88cc7218f63973c940d1f25.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
On the fitting ideals of a comultiplication module
31
39
EN
S.
Karimzadeh
Vali-e-Asr University of Rafsanjan
karimzadeh@vru.ac.ir
S.
Hadjirezaei
Vali-e-Asr University of Rafsanjan
s.hajirezaei@vru.ac.ir
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
http://jart.guilan.ac.ir/article_1211.html
http://jart.guilan.ac.ir/article_1211_33e4f18032e4525d4779c336be03ffab.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
F-regularity relative to modules
41
50
EN
F.
Dorostkar
University of Guilan
dorostkar@guilan.ac.ir
R.
khosravi
University of Guilan
khosravi@phd.guilan.ac.ir
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
http://jart.guilan.ac.ir/article_1212.html
http://jart.guilan.ac.ir/article_1212_1707024d6a7b82e8d1892f7dbb86f9ff.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
A note on maximal non-prime ideals
51
61
EN
S.
Visweswaran
Saurashtra University
visweswaran2006@yahoo.co.in
A.
Parmar
Saurashtra University
anirudh.maths@gmail.com
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
http://jart.guilan.ac.ir/article_1213.html
http://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
3
1
2015
07
16
Some numerical results on two classes of finite groups
63
72
EN
M.
Hashemi
University of Guilan
m_hashemi@guilan.ac.ir
M.
Polkouei
University of Guilan
mikhakp@yahoo.com
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
http://jart.guilan.ac.ir/article_1214.html
http://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf