2017
5
1
0
82
Good strongly regular relations on weak $Gamma$(semi)hypergroups
2
2
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.
1

1
10


M.
Jafarpour
ValieAsr university of Rafsanjan
ValieAsr university of Rafsanjan
Iran
rmo4909@yahoo.com


H.
Aghabozorgi
ValieAsr university of Rafsanjan
ValieAsr university of Rafsanjan
Iran
h_aghabozorgi1@yahoo.com


T.
Zare
ValieAsr university of Rafsanjan
ValieAsr university of Rafsanjan
Iran
tahere_zare@yahoo.com
(semi)hypergroup
weak $Gamma$(semi)hypergroup
good regular relation
Left Iquotients of band of right cancellative monoids
2
2
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left Iorder in $Q$ and $Q$ is a semigroup of left Iquotients 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 Iquotients of left regular bands of right cancellative monoids with certain conditions.
1

11
25


N.
Ghroda
AlGhrabi University
AlGhrabi University
Libya
nassraddin2010@gmail.com
Iorders
Iquotients
right cancellative monoid
inverse hull
Exact annihilatingideal graph of commutative rings
2
2
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 annihilatingideal graph of commutative rings. We discuss the interplay between the ringtheoretic properties of a ring and graphtheoretic properties of exact annihilatingideal graph of the ring.
1

27
33


P. T.
Lalchandani
Sauarshtra University
Sauarshtra University
India
finiteuniverse@live.com
Annihilatingideal graph
exact annihilatingideal
exact annihilatingideal graph
A new branch of the logical algebra: UPalgebras
2
2
In this paper, we introduce a new algebraic structure, called a UPalgebra (UP means the University of Phayao) and a concept of UPideals, UPsubalgebras, congruences and UPhomomorphisms in UPalgebras, and investigated some related properties of them. We also describe connections between UPideals, UPsubalgebras, congruences and UPhomomorphisms, and show that the notion of UPalgebras is a generalization of KUalgebras.
1

35
54


A.
Iampan
University of Phayao
University of Phayao
Thailand
aiyared.ia@up.ac.th
UPalgebra
UPideal
congruence
UPhomomorphism
Properties of extended ideal based zero divisor graph of a commutative ring
2
2
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 $overline Gamma_I(R)$.
1

52
59


K.
Porselvi
Karunya University
Karunya University
India
porselvi94@yahoo.co.in


R.
Solomon Jones
Karunya University
Karunya University
India
jonesrooneya@gmail.com
Commutative rings
ideals
prime ideals
zerodivisor graph
A Note on a graph associated to a commutative ring
2
2
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.
1

61
82


S.
Visweswaran
Saurashtra University
Saurashtra University
Indian
s_visweswaran2006@yahoo.co.in


J.
Parejiya
Saurashtra University
Saurashtra University
India
parejiayjay@gmail.com
Comaximal graph of a ring
complete graph
chromatic number
clique number
planar graph