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Journal of Algebra and Related Topics最新文献

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Some results on a subgraph of the intersection graph of ideals of a commutative ring 交换环理想交图子图的一些结果
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/JART.2018.11188.1114
S. Visweswaran, P. Vadhel
{"title":"Some results on a subgraph of the intersection graph of ideals of a commutative ring","authors":"S. Visweswaran, P. Vadhel","doi":"10.22124/JART.2018.11188.1114","DOIUrl":"https://doi.org/10.22124/JART.2018.11188.1114","url":null,"abstract":"The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal.   Let $R$ be a ring. Let us denote  the collection  of all proper ideals  of $R$ by $mathbb{I}(R)$  and $mathbb{I}(R)backslash {(0)}$ by $mathbb{I}(R)^{*}$.  With $R$, we associate an undirected graph denoted by $g(R)$, whose vertex set is $mathbb{I}(R)^{*}$ and distinct vertices $I_{1}, I_{2}$ are adjacent in $g(R)$  if and only if $I_{1}cap I_{2}neq I_{1}I_{2}$.  The aim of this article is to study the interplay between the graph-theoretic properties of $g(R)$ and the ring-theoretic properties of $R$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"35-61"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43994065","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}
引用次数: 1
On the ranks of certain semigroups of order-preserving partial isometries of a finite chain 有限链上保序部分等距的某些半群的秩
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/JART.2019.10875.1109
B. Ali, M. A. Jada, M. M. Zubairu
{"title":"On the ranks of certain semigroups of order-preserving partial isometries of a finite chain","authors":"B. Ali, M. A. Jada, M. M. Zubairu","doi":"10.22124/JART.2019.10875.1109","DOIUrl":"https://doi.org/10.22124/JART.2019.10875.1109","url":null,"abstract":"Let $X_n={1,2,ldots,n}$ be a finite chain, $mathcal{ODP}_{n}$ be the semigroup of order-preserving partial isometries on $X_n$ and $N$ be the set of all nilpotents in $mathcal{ODP}_{n}$. In this work, we study the nilpotents in $mathcal{ODP}_{n}$ and investigate the ranks of two subsemigroups of $mathcal{ODP}_{n}$; the nilpotent generatedsubsemigroup $langle Nrangle$ and the subsemigroup ~$L(n,r)= { alpha in mathcal{ODP}_{n} : |im~alpha|leq r}$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"15-33"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44537344","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}
引用次数: 2
Classical Zariski Topology on Prime Spectrum of Lattice Modules 格模素数谱上的经典Zariski拓扑
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/JART.2018.11106.1112
V. Borkar, P. Girase, Narayan Phadatare
{"title":"Classical Zariski Topology on Prime Spectrum of Lattice Modules","authors":"V. Borkar, P. Girase, Narayan Phadatare","doi":"10.22124/JART.2018.11106.1112","DOIUrl":"https://doi.org/10.22124/JART.2018.11106.1112","url":null,"abstract":"Let $M$ be a lattice module over a  $C$-lattice $L$.  Let $Spec^{p}(M)$ be the collection of all prime elements of $M$. In this article, we consider a  topology on $Spec^{p}(M)$, called the classical Zariski topology and investigate the topological properties of $Spec^{p}(M)$ and the algebraic properties of $M$. We investigate this topological space from the point of view of spectral spaces.  By  Hochster's characterization of a spectral space, we show that for each lattice module $M$ with finite spectrum, $Spec^{p}(M)$ is a spectral space. Also we introduce finer patch topology on $Spec^{p}(M)$ and we show that $Spec^{p}(M)$ with finer patch topology is a compact space and every irreducible closed subset of $Spec^{p}(M)$ (with classical Zariski topology) has a generic point  and $Spec^{p}(M)$ is a spectral space, for a lattice module $M$ which has ascending chain condition on prime radical elements.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"1-14"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48058263","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}
引用次数: 1
Essential subhypermodules and their properties 本质子超模及其性质
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.9573.1089
B. Talaee
{"title":"Essential subhypermodules and their properties","authors":"B. Talaee","doi":"10.22124/JART.2018.9573.1089","DOIUrl":"https://doi.org/10.22124/JART.2018.9573.1089","url":null,"abstract":"Let R be a hyperring (in the sense of [8]) andM be a hypermodule on R. In this paper we will introduce and study a class of subhypermodules of M. We will study on intersection of this kind of subhypermodules a give some suitable results about them. We will proceed to give some in- teresting results about the complements, direct sums and independency of this kind of subhypermodules.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"55-66"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42233444","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}
引用次数: 0
Identities in $3$-prime near-rings with left multipliers 具有左乘子的3素数近环的恒等式
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.10093.1096
M. Ashraf, A. Boua
{"title":"Identities in $3$-prime near-rings with left multipliers","authors":"M. Ashraf, A. Boua","doi":"10.22124/JART.2018.10093.1096","DOIUrl":"https://doi.org/10.22124/JART.2018.10093.1096","url":null,"abstract":"Let $mathcal{N}$ be a $3$-prime near-ring with the center$Z(mathcal{N})$ and $n geq 1$ be a fixed positive integer. Inthe present paper it is shown that a $3$-prime near-ring$mathcal{N}$ is a commutative ring if and only if it admits aleft multiplier $mathcal{F}$ satisfying any one of the followingproperties: $(i):mathcal{F}^{n}([x, y])in Z(mathcal{N})$, $(ii):mathcal{F}^{n}(xcirc y)in Z(mathcal{N})$,$(iii):mathcal{F}^{n}([x, y])pm(xcirc y)in Z(mathcal{N})$ and $(iv):mathcal{F}^{n}([x, y])pm xcirc yin Z(mathcal{N})$, for all $x, yinmathcal{N}$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"67-77"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48251982","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}
引用次数: 2
A note on the extended total graph of commutative rings 交换环的扩展全图的一个注记
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.10241.1101
F. Saraei, E. Navidinia
{"title":"A note on the extended total graph of commutative rings","authors":"F. Saraei, E. Navidinia","doi":"10.22124/JART.2018.10241.1101","DOIUrl":"https://doi.org/10.22124/JART.2018.10241.1101","url":null,"abstract":"Let $R$ be a commutative ring and $H$ a nonempty proper subset of $R$.In this paper, the extended total graph, denoted by $ET_{H}(R)$ is presented, where $H$ is amultiplicative-prime subset of $R$. It is the graph with all elements of $R$ as vertices, and for distinct $p,qin R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sqin H$ for some $r,sin Rsetminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(Rsetminus H)$, with vertices $H$ and $Rsetminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"25-33"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44395720","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}
引用次数: 1
Non-reduced rings of small order and their maximal graph 小阶非约环及其极大图
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.10130.1097
Arti Sharma, A. Gaur
{"title":"Non-reduced rings of small order and their maximal graph","authors":"Arti Sharma, A. Gaur","doi":"10.22124/JART.2018.10130.1097","DOIUrl":"https://doi.org/10.22124/JART.2018.10130.1097","url":null,"abstract":"Let $R$ be a commutative ring with nonzero identity. Let $Gamma(R)$ denotes the maximal graph corresponding to the non-unit elements of R, that is, $Gamma(R)$is a graph with vertices the non-unit elements of $R$, where two distinctvertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$containing both. In this paper, we investigate that for a given positive integer $n$, is there a non-reduced ring $R$ with $n$ non-units? For $n leq 100$, a complete list of non-reduced decomposable rings $R = prod_{i=1}^{k}R_i$ (up to cardinalities of constituent local rings $R_i$'s) with n non-units is given. We also show that for which $n$, $(1leq n leq 7500)$, $|Center(Gamma(R))|$ attains the bounds in the inequality $1leq |Center(Gamma(R))|leq n$ and for which $n$, $(2leq nleq 100)$, $|Center(Gamma(R))|$ attains the value between the bounds","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"35-44"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46721966","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}
引用次数: 0
$mathcal{N}$-Fuzzy UP-Algebras and its level subsets $math{N}$-Fuzzy UP代数及其水平子集
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.10280.1102
M. Songsaeng, Aiyared Iampan
{"title":"$mathcal{N}$-Fuzzy UP-Algebras and its level subsets","authors":"M. Songsaeng, Aiyared Iampan","doi":"10.22124/JART.2018.10280.1102","DOIUrl":"https://doi.org/10.22124/JART.2018.10280.1102","url":null,"abstract":"In this paper, $mathcal{N}$-fuzzy UP-subalgebras (resp., $mathcal{N}$-fuzzy UP-filters, $mathcal{N}$-fuzzy UP-ideals and $mathcal{N}$-fuzzy strongly UP-ideals) of UP-algebras are introduced and considered their generalizations and characteristic $mathcal{N}$-fuzzy sets of UP-subalgebras (resp., UP-filters, UP-ideals and strongly UP-ideals).Further, we discuss the relations between $mathcal{N}$-fuzzy UP-subalgebras (resp., $mathcal{N}$-fuzzy UP-filters, $mathcal{N}$-fuzzy UP-ideals and $mathcal{N}$-fuzzy strongly UP-ideals) and its level subsets.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"1-24"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49482805","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}
引用次数: 11
Tight Closure of a Graded Ideal Relative to a Graded Module 分次理想相对于分次模的紧闭包
Journal of Algebra and Related Topics Pub Date : 2018-06-01 DOI: 10.22124/JART.2018.9589.1092
F. Dorostkar, R. Khosravi
{"title":"Tight Closure of a Graded Ideal Relative to a Graded Module","authors":"F. Dorostkar, R. Khosravi","doi":"10.22124/JART.2018.9589.1092","DOIUrl":"https://doi.org/10.22124/JART.2018.9589.1092","url":null,"abstract":"In this paper we will study the tight closure of a graded ideal relative to a graded Module.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"45-54"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48754629","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}
引用次数: 0
On the additive maps satisfying Skew-Engel conditions 在满足Skew-Engel条件的加性映射上
Journal of Algebra and Related Topics Pub Date : 2017-12-01 DOI: 10.22124/JART.2017.2715
M. Nadeem, M. Aslam, Y. Ahmed
{"title":"On the additive maps satisfying Skew-Engel conditions","authors":"M. Nadeem, M. Aslam, Y. Ahmed","doi":"10.22124/JART.2017.2715","DOIUrl":"https://doi.org/10.22124/JART.2017.2715","url":null,"abstract":"Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"5 1","pages":"47-58"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43038917","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}
引用次数: 1
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