@Article{Jafarpour2017,
author="Jafarpour, M.
and Aghabozorgi, H.
and Zare, T.",
title="Good strongly regular relations on weak $\Gamma$-(semi)hypergroups",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="1-10",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2401",
url="http://jart.guilan.ac.ir/article_2401.html"
}
@Article{Ghroda2017,
author="Ghroda, N.",
title="Left I-quotients of band of right cancellative monoids",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="11-25",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2402",
url="http://jart.guilan.ac.ir/article_2402.html"
}
@Article{Lalchandani2017,
author="Lalchandani, P. T.",
title="Exact annihilating-ideal graph of commutative rings",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="27-33",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2400",
url="http://jart.guilan.ac.ir/article_2400.html"
}
@Article{Iampan2017,
author="Iampan, A.",
title="A new branch of the logical algebra: UP-algebras",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="35-54",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2403",
url="http://jart.guilan.ac.ir/article_2403.html"
}
@Article{Porselvi2017,
author="Porselvi, K.
and Solomon Jones, R.",
title="Properties of extended ideal based zero divisor graph of a commutative ring",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="52-59",
abstract="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 $\overline \Gamma_I(R)$.",
issn="2345-3931",
doi="10.22124/jart.2017.2404",
url="http://jart.guilan.ac.ir/article_2404.html"
}
@Article{Visweswaran2017,
author="Visweswaran, S.
and Parejiya, J.",
title="A Note on a graph associated to a commutative ring",
journal="Journal of Algebra and Related Topics",
year="2017",
volume="5",
number="1",
pages="61-82",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2017.2399",
url="http://jart.guilan.ac.ir/article_2399.html"
}