ORIGINAL_ARTICLE
Good strongly regular relations on weak $\Gamma$-(semi)hypergroups
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.
http://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
1
10
10.22124/jart.2017.2401
(semi)hypergroup
weak $Gamma$-(semi)hypergroup
good regular relation
M.
Jafarpour
rmo4909@yahoo.com
true
1
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
LEAD_AUTHOR
H.
Aghabozorgi
h_aghabozorgi1@yahoo.com
true
2
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
AUTHOR
T.
Zare
tahere_zare@yahoo.com
true
3
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
Vali-e-Asr university of Rafsanjan
AUTHOR
ORIGINAL_ARTICLE
Left I-quotients of band of right cancellative monoids
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.
http://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
11
25
10.22124/jart.2017.2402
I-orders
I-quotients
right cancellative monoid
inverse hull
N.
Ghroda
nassraddin2010@gmail.com
true
1
Al-Ghrabi University
Al-Ghrabi University
Al-Ghrabi University
LEAD_AUTHOR
ORIGINAL_ARTICLE
Exact annihilating-ideal graph of commutative rings
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.
http://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
27
33
10.22124/jart.2017.2400
Annihilating-ideal graph
exact annihilating-ideal
exact annihilating-ideal graph
P. T.
Lalchandani
finiteuniverse@live.com
true
1
Sauarshtra University
Sauarshtra University
Sauarshtra University
LEAD_AUTHOR
ORIGINAL_ARTICLE
A new branch of the logical algebra: UP-algebras
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.
http://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
35
54
10.22124/jart.2017.2403
UP-algebra
UP-ideal
congruence
UP-homomorphism
A.
Iampan
aiyared.ia@up.ac.th
true
1
University of Phayao
University of Phayao
University of Phayao
LEAD_AUTHOR
ORIGINAL_ARTICLE
Properties of extended ideal based zero divisor graph of a commutative ring
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 $\overline \Gamma_I(R)$.
http://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
52
59
10.22124/jart.2017.2404
Commutative rings
ideals
prime ideals
zero-divisor graph
K.
Porselvi
porselvi94@yahoo.co.in
true
1
Karunya University
Karunya University
Karunya University
LEAD_AUTHOR
R.
Solomon Jones
jonesrooneya@gmail.com
true
2
Karunya University
Karunya University
Karunya University
AUTHOR
ORIGINAL_ARTICLE
A Note on a graph associated to a commutative ring
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.
http://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf
2017-06-01T11:23:20
2018-08-16T11:23:20
61
82
10.22124/jart.2017.2399
Comaximal graph of a ring
complete graph
chromatic number
clique number
planar graph
S.
Visweswaran
s_visweswaran2006@yahoo.co.in
true
1
Saurashtra University
Saurashtra University
Saurashtra University
LEAD_AUTHOR
J.
Parejiya
parejiayjay@gmail.com
true
2
Saurashtra University
Saurashtra University
Saurashtra University
AUTHOR