eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
1
10
10.22124/jart.2017.2401
2401
مقاله پژوهشی
Good strongly regular relations on weak $Gamma$-(semi)hypergroups
M. Jafarpour
rmo4909@yahoo.com
1
H. Aghabozorgi
h_aghabozorgi1@yahoo.com
2
T. Zare
tahere_zare@yahoo.com
3
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
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.
https://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf
(semi)hypergroup
weak $Gamma$-(semi)hypergroup
good regular relation
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
11
25
10.22124/jart.2017.2402
2402
مقاله پژوهشی
Left I-quotients of band of right cancellative monoids
N. Ghroda
nassraddin2010@gmail.com
1
Al-Ghrabi University
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.
https://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf
I-orders
I-quotients
right cancellative monoid
inverse hull
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
27
33
10.22124/jart.2017.2400
2400
مقاله پژوهشی
Exact annihilating-ideal graph of commutative rings
P. T. Lalchandani
finiteuniverse@live.com
1
Sauarshtra University
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.
https://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf
Annihilating-ideal graph
exact annihilating-ideal
exact annihilating-ideal graph
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
35
54
10.22124/jart.2017.2403
2403
مقاله پژوهشی
A new branch of the logical algebra: UP-algebras
A. Iampan
aiyared.ia@up.ac.th
1
University of Phayao
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.
https://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf
UP-algebra
UP-ideal
congruence
UP-homomorphism
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
52
59
10.22124/jart.2017.2404
2404
مقاله پژوهشی
Properties of extended ideal based zero divisor graph of a commutative ring
K. Porselvi
porselvi94@yahoo.co.in
1
R. Solomon Jones
jonesrooneya@gmail.com
2
Karunya University
Karunya University
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 $overline Gamma_I(R)$.
https://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdf
Commutative rings
ideals
prime ideals
zero-divisor graph
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2017-06-01
5
1
61
82
10.22124/jart.2017.2399
2399
مقاله پژوهشی
A Note on a graph associated to a commutative ring
S. Visweswaran
s_visweswaran2006@yahoo.co.in
1
J. Parejiya
parejiayjay@gmail.com
2
Saurashtra University
Saurashtra University
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.
https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf
Comaximal graph of a ring
complete graph
chromatic number
clique number
planar graph