{"title":"Algebraic adjoint of the polynomials-polynomial matrix multiplication","authors":"R. Andriamifidisoa, H. Randriambolasata","doi":"10.22124/JART.2017.2713","DOIUrl":"https://doi.org/10.22124/JART.2017.2713","url":null,"abstract":"This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"25-33"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49257998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Self-cogenerator modules and their applications","authors":"Y. Talebi, M. Hosseinpour","doi":"10.22124/JART.2017.2716","DOIUrl":"https://doi.org/10.22124/JART.2017.2716","url":null,"abstract":"Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we give some properties of self-cogeneratormodules. If $M$ is self-cogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a$mathcal{K}$-module. It is shown that every self-cogenerator Baer is dual Baer.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"59-68"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44372082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$G$-Weights and $p$-Local Rank","authors":"P. D. Wade","doi":"10.22124/JART.2017.2711","DOIUrl":"https://doi.org/10.22124/JART.2017.2711","url":null,"abstract":"Let $k$ be field of characteristic $p$, andlet $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.In this paper, we introduce the notion of radical $B$-chain $C_{B}$, and we show that the $p$-local rank of $B$ is equals the length of $C_{B}$. Moreover, we prove that the vertex of a simple $kG$-module $S$ is radical if and only if it has the same vertex of the unique direct summand, up to isomorphism, of the Sylow permutationmodule whose radical quotient is isomorphic to $S$. Finally, we prove the vertices of certain direct summands of the Sylow permutation module are bounds for the vertices of simple $kG$-modules.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48182538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"σ-sporadic prime ideals and superficial elements","authors":"D. Kamano, K. A. Essan, A. Abdoulaye, E. D. Akeke","doi":"10.22124/JART.2017.2714","DOIUrl":"https://doi.org/10.22124/JART.2017.2714","url":null,"abstract":"Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I)$, with $n$ small, which are the sets of $sigma$-sporadic prime divisors of $I$.We also give some relationships between $sigma(f_I)$-superficial elements and asymptotic prime $sigma$-divisors, where $sigma (f_I)$ is the $sigma$-closure of the $I$-adic filtration $f_I=(I^n)_{ninmathbb{N}}$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"35-45"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43237343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Good strongly regular relations on weak $Gamma$-(semi)hypergroups","authors":"M. Jafarpour, H. Aghabozorgi, T. Zare","doi":"10.22124/JART.2017.2401","DOIUrl":"https://doi.org/10.22124/JART.2017.2401","url":null,"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.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"11 3","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41285908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Left I-quotients of band of right cancellative monoids","authors":"N. Ghroda","doi":"10.22124/JART.2017.2402","DOIUrl":"https://doi.org/10.22124/JART.2017.2402","url":null,"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 $qin Q$ 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 I-quotients of left regular bands of right cancellative monoids with certain conditions.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"11-25"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48558024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Properties of extended ideal based zero divisor graph of a commutative ring","authors":"K. Porselvi, R. Jones","doi":"10.22124/JART.2017.2404","DOIUrl":"https://doi.org/10.22124/JART.2017.2404","url":null,"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 $overline Gamma_I(R)$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"52-59"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47840291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact annihilating-ideal graph of commutative rings","authors":"P. T. Lalchandani","doi":"10.22124/jart.2017.2400","DOIUrl":"https://doi.org/10.22124/jart.2017.2400","url":null,"abstract":"The rings considered in this article are commutative rings with identity 1 6= 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.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"27-33"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46585417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new branch of the logical algebra: UP-algebras","authors":"Aiyared Iampan","doi":"10.22124/JART.2017.2403","DOIUrl":"https://doi.org/10.22124/JART.2017.2403","url":null,"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.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"35-54"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46235621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Note on a graph associated to a commutative ring","authors":"S. Visweswaran, J. Parejiya","doi":"10.22124/JART.2017.2399","DOIUrl":"https://doi.org/10.22124/JART.2017.2399","url":null,"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 $Rxcap Ry = Rxy$. 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.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"61-82"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46860996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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