University of GuilanJournal of Algebra and Related Topics2345-39315120170601Good strongly regular relations on weak $\Gamma$-(semi)hypergroups110240110.22124/jart.2017.2401ENM.JafarpourVali-e-Asr university of RafsanjanH.AghabozorgiVali-e-Asr university of RafsanjanT.ZareVali-e-Asr university of RafsanjanJournal Article20170106In 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.<br /><br />https://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315120170601Left I-quotients of band of right cancellative monoids1125240210.22124/jart.2017.2402ENN.GhrodaAl-Ghrabi UniversityJournal Article20170307Let $Q$ 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.<br /><br />https://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315120170601Exact annihilating-ideal graph of commutative rings2733240010.22124/jart.2017.2400ENP. T.LalchandaniSauarshtra University0000-0001-8938-7552Journal Article20161123The 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.https://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315120170601A new branch of the logical algebra: UP-algebras3554240310.22124/jart.2017.2403ENA.IampanUniversity of Phayao0000-0002-0475-3320Journal Article20170314In 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.<br /> 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.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315120170601Properties of extended ideal based zero divisor graph of a commutative ring5259240410.22124/jart.2017.2404ENK.PorselviKarunya Universityhttp://orcid.org/000R.Solomon JonesKarunya UniversityJournal Article20170502This 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 $\overline \Gamma_I(R)$.<br /><br />https://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39315120170601A Note on a graph associated to a commutative ring6182239910.22124/jart.2017.2399ENS.VisweswaranSaurashtra UniversityJ.ParejiyaSaurashtra UniversityJournal Article20170806The 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.<br /><br />https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf