2018-01-24T12:51:15Z
http://jart.guilan.ac.ir/?_action=export&rf=summon&issue=445
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
Good strongly regular relations on weak $Gamma$-(semi)hypergroups
M.
Jafarpour
H.
Aghabozorgi
T.
Zare
In this paper first we introduce the notion of weak $Gamma$-(semi)hypergroups, next some classes of equivalence relations which are called good regular and strongly good regular relations are defined. Then we investigate some properties of this kind of relations on weak $Gamma$-(semi)hypergroups.
(semi)hypergroup
weak $Gamma$-(semi)hypergroup
good regular relation
2017
09
01
1
10
http://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
Left I-quotients of band of right cancellative monoids
N.
Ghroda
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancellative monoids with certain conditions.
I-orders
I-quotients
right cancellative monoid
inverse hull
2017
09
01
11
25
http://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
Exact annihilating-ideal graph of commutative rings
P. T.
Lalchandani
The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
Annihilating-ideal graph
exact annihilating-ideal
exact annihilating-ideal graph
2017
09
01
27
33
http://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
A new branch of the logical algebra: UP-algebras
A.
Iampan
In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a generalization of KU-algebras.
UP-algebra
UP-ideal
congruence
UP-homomorphism
2017
09
01
35
54
http://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
Properties of extended ideal based zero divisor graph of a commutative ring
K.
Porselvi
R.
Solomon Jones
This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.
Commutative rings
ideals
prime ideals
zero-divisor graph
2017
09
01
52
59
http://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdf
Journal of Algebra and Related Topics
2345-3931
2345-3931
2017
5
1
A Note on a graph associated to a commutative ring
S.
Visweswaran
J.
Parejiya
The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $chi(G(R)) = omega(G(R))< infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.
Comaximal graph of a ring
complete graph
chromatic number
clique number
planar graph
2017
09
01
61
82
http://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf