Good strongly regular relations on weak $\Gamma$-(semi)hypergroups
M.
Jafarpour
Vali-e-Asr university of Rafsanjan
author
H.
Aghabozorgi
Vali-e-Asr university of Rafsanjan
author
T.
Zare
Vali-e-Asr university of Rafsanjan
author
text
article
2017
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
1
10
http://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf
Left I-quotients of band of right cancellative monoids
N.
Ghroda
Al-Ghrabi University
author
text
article
2017
eng
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 $q\in Q$ can be written as $q=a^{-1}b$ for some $a,b\in S$. 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
11
25
http://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf
Exact annihilating-ideal graph of commutative rings
P. T.
Lalchandani
Sauarshtra University
author
text
article
2017
eng
The rings considered in this article are commutative rings with identity $1\neq 0$. 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
27
33
http://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf
A new branch of the logical algebra: UP-algebras
A.
Iampan
University of Phayao
author
text
article
2017
eng
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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
35
54
http://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf
Properties of extended ideal based zero divisor graph of a commutative ring
K.
Porselvi
Karunya University
author
R.
Solomon Jones
Karunya University
author
text
article
2017
eng
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 $\overline \Gamma_I(R)$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
52
59
http://jart.guilan.ac.ir/article_2404_dfe70b9e955819ccf6b751206f3b9e95.pdf
A Note on a graph associated to a commutative ring
S.
Visweswaran
Saurashtra University
author
J.
Parejiya
Saurashtra University
author
text
article
2017
eng
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 $Rx\cap Ry = Rxy$. 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.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
5
v.
1
no.
2017
61
82
http://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf