Line graphs associated to the maximal graph
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
A. Sharma,A. Gaur
University of Delhi,University of Delhi
1
Maximal graph,line graph,eulerian graph,comaximal graph
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.
http://jart.guilan.ac.ir/article_1209.html
http://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdf
Strongly cotop modules
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
H. Ansari-Toroghy,S.S. Pourmortazavi,S. Keyvani
University of Guilan,University of Guilan,Islamic Azad University
13
Second submodule,strongly cotop module,Zariski topology,spectral space
In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.
http://jart.guilan.ac.ir/article_1210.html
http://jart.guilan.ac.ir/article_1210_4cce280ab88cc7218f63973c940d1f25.pdf
On the fitting ideals of a comultiplication module
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
S. Karimzadeh,S. Hadjirezaei
Vali-e-Asr University of Rafsanjan,Vali-e-Asr University of Rafsanjan
31
Fitting ideals,comultiplication module,simple module
Let $R$ be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.
http://jart.guilan.ac.ir/article_1211.html
http://jart.guilan.ac.ir/article_1211_33e4f18032e4525d4779c336be03ffab.pdf
F-regularity relative to modules
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
F. Dorostkar,R. khosravi
University of Guilan,University of Guilan
41
Tight closure,$F-$regular,and weakly $F-$regular relative to a module
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 .
http://jart.guilan.ac.ir/article_1212.html
http://jart.guilan.ac.ir/article_1212_1707024d6a7b82e8d1892f7dbb86f9ff.pdf
A note on maximal non-prime ideals
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
S. Visweswaran,A. Parmar
Saurashtra University,Saurashtra University
51
Maximal non-prime ideal,maximal non-maximal ideal,maximal non-primary ideal,maximal non-irreducible ideal
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 $R$.
http://jart.guilan.ac.ir/article_1213.html
http://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf
Some numerical results on two classes of finite groups
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015
07
3
1
No
2015-07-16
M. Hashemi,M. Polkouei
University of Guilan,University of Guilan
63
Nilpotent groups,$n^{th}$-commutativity degree,$n$-abelian groups
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 $g.c.d(s,l)=1$.
http://jart.guilan.ac.ir/article_1214.html
http://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf