eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
1
11
1209
مقاله پژوهشی
Line graphs associated to the maximal graph
A. Sharma
anirudh.maths@gmail.com
1
A. Gaur
gaursatul@gmail.com
2
University of Delhi
University of Delhi
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.
https://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdf
Maximal graph
line graph
eulerian graph
comaximal graph
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
13
29
1210
مقاله پژوهشی
Strongly cotop modules
H. Ansari-Toroghy
ansari@guilan.ac.ir
1
S.S. Pourmortazavi
mortazavi@phd.guilan.ac.ir
2
S. Keyvani
keivani@bandaranzaliiau.ac.ir
3
University of Guilan
University of Guilan
Islamic Azad University
In 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.pdf
Second submodule
strongly cotop module
Zariski topology
spectral space
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
31
39
1211
مقاله پژوهشی
On the fitting ideals of a comultiplication module
S. Karimzadeh
karimzadeh@vru.ac.ir
1
S. Hadjirezaei
s.hajirezaei@vru.ac.ir
2
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
Let $R$ 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.pdf
Fitting ideals
comultiplication module
simple module
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
41
50
1212
مقاله پژوهشی
F-regularity relative to modules
F. Dorostkar
dorostkar@guilan.ac.ir
1
R. khosravi
khosravi@phd.guilan.ac.ir
2
University of Guilan
University of Guilan
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 .
https://jart.guilan.ac.ir/article_1212_1707024d6a7b82e8d1892f7dbb86f9ff.pdf
Tight closure
$F-$regular
and weakly $F-$regular relative to a module
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
51
61
1213
مقاله پژوهشی
A note on maximal non-prime ideals
S. Visweswaran
visweswaran2006@yahoo.co.in
1
A. Parmar
anirudh.maths@gmail.com
2
Saurashtra University
Saurashtra University
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 $R$.
https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf
Maximal non-prime ideal
maximal non-maximal ideal
maximal non-primary ideal
maximal non-irreducible ideal
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2015-06-01
3
1
63
72
1214
مقاله پژوهشی
Some numerical results on two classes of finite groups
M. Hashemi
m_hashemi@guilan.ac.ir
1
M. Polkouei
mikhakp@yahoo.com
2
University of Guilan
University of Guilan
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 $g.c.d(s,l)=1$.
https://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf
Nilpotent groups
$n^{th}$-commutativity degree
$n$-abelian groups