ORIGINAL_ARTICLE
Line graphs associated to the maximal 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.
https://jart.guilan.ac.ir/article_1209_6febd2a7a22b03870dcd02ddde00b032.pdf
2015-06-01T11:23:20
2019-04-22T11:23:20
1
11
Maximal graph
line graph
eulerian graph
comaximal graph
A.
Sharma
anirudh.maths@gmail.com
true
1
University of Delhi
University of Delhi
University of Delhi
AUTHOR
A.
Gaur
gaursatul@gmail.com
true
2
University of Delhi
University of Delhi
University of Delhi
LEAD_AUTHOR
ORIGINAL_ARTICLE
Strongly cotop modules
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
2015-06-01T11:23:20
2019-04-22T11:23:20
13
29
Second submodule
strongly cotop module
Zariski topology
spectral space
H.
Ansari-Toroghy
ansari@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
S.S.
Pourmortazavi
mortazavi@phd.guilan.ac.ir
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR
S.
Keyvani
keivani@bandaranzaliiau.ac.ir
true
3
Islamic Azad University
Islamic Azad University
Islamic Azad University
AUTHOR
ORIGINAL_ARTICLE
On the fitting ideals of a comultiplication module
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
2015-06-01T11:23:20
2019-04-22T11:23:20
31
39
Fitting ideals
comultiplication module
simple module
S.
Karimzadeh
karimzadeh@vru.ac.ir
true
1
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
LEAD_AUTHOR
S.
Hadjirezaei
s.hajirezaei@vru.ac.ir
true
2
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
AUTHOR
ORIGINAL_ARTICLE
F-regularity relative to modules
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
2015-06-01T11:23:20
2019-04-22T11:23:20
41
50
Tight closure
$F-$regular
and weakly $F-$regular relative to a module
F.
Dorostkar
dorostkar@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
R.
khosravi
khosravi@phd.guilan.ac.ir
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR
ORIGINAL_ARTICLE
A note on maximal non-prime ideals
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 $R$.
https://jart.guilan.ac.ir/article_1213_ef7c4b9f1125da4eb7d276b1d9cbcb6d.pdf
2015-06-01T11:23:20
2019-04-22T11:23:20
51
61
Maximal non-prime ideal
maximal non-maximal ideal
maximal non-primary ideal
maximal non-irreducible ideal
S.
Visweswaran
visweswaran2006@yahoo.co.in
true
1
Saurashtra University
Saurashtra University
Saurashtra University
LEAD_AUTHOR
A.
Parmar
anirudh.maths@gmail.com
true
2
Saurashtra University
Saurashtra University
Saurashtra University
AUTHOR
ORIGINAL_ARTICLE
Some numerical results on two classes of finite groups
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=\langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]\rangle $$$$K(s,l)=\langle a,b|ab^s=b^la,~ba^s=a^lb\rangle;$$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 $g.c.d(s,l)=1$.
https://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf
2015-06-01T11:23:20
2019-04-22T11:23:20
63
72
Nilpotent groups
$n^{th}$-commutativity degree
$n$-abelian groups
M.
Hashemi
m_hashemi@guilan.ac.ir
true
1
University of Guilan
University of Guilan
University of Guilan
LEAD_AUTHOR
M.
Polkouei
mikhakp@yahoo.com
true
2
University of Guilan
University of Guilan
University of Guilan
AUTHOR