@article { 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}, volume = {5}, number = {1}, pages = {1-10}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2401}, 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.}, keywords = {(semi)hypergroup,weak $Gamma$-(semi)hypergroup,good regular relation}, url = {https://jart.guilan.ac.ir/article_2401.html}, eprint = {https://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf} } @article { author = {Ghroda, N.}, title = {Left I-quotients of band of right cancellative monoids}, journal = {Journal of Algebra and Related Topics}, volume = {5}, number = {1}, pages = {11-25}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2402}, 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.}, keywords = {I-orders,I-quotients,right cancellative monoid,inverse hull}, url = {https://jart.guilan.ac.ir/article_2402.html}, eprint = {https://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf} } @article { author = {Lalchandani, P. T.}, title = {Exact annihilating-ideal graph of commutative rings}, journal = {Journal of Algebra and Related Topics}, volume = {5}, number = {1}, pages = {27-33}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2400}, 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.}, keywords = {Annihilating-ideal graph,exact annihilating-ideal,exact annihilating-ideal graph}, url = {https://jart.guilan.ac.ir/article_2400.html}, eprint = {https://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf} } @article { author = {Iampan, A.}, title = {A new branch of the logical algebra: UP-algebras}, journal = {Journal of Algebra and Related Topics}, volume = {5}, number = {1}, pages = {35-54}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2403}, 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.}, keywords = {UP-algebra,UP-ideal,congruence,UP-homomorphism}, url = {https://jart.guilan.ac.ir/article_2403.html}, eprint = {https://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf} } @article { 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}, volume = {5}, number = {1}, pages = {52-59}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2404}, 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 $\overline \Gamma_I(R)$.}, keywords = {Commutative rings,ideals,prime ideals,zero-divisor graph}, url = {https://jart.guilan.ac.ir/article_2404.html}, eprint = {https://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdf} } @article { author = {Visweswaran, S. and Parejiya, J.}, title = {A Note on a graph associated to a commutative ring}, journal = {Journal of Algebra and Related Topics}, volume = {5}, number = {1}, pages = {61-82}, year = {2017}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2017.2399}, 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.}, keywords = {Comaximal graph of a ring,complete graph,chromatic number,clique number,planar graph}, url = {https://jart.guilan.ac.ir/article_2399.html}, eprint = {https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf} }