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Journal of Algebra and Related Topics最新文献

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A new generalization of t-lifting modules t-提升模的一个新推广
Journal of Algebra and Related Topics Pub Date : 2020-06-01 DOI: 10.22124/JART.2020.16482.1203
Y. Talebi, A. R. M. Hamzekolaee, M. Hosseinpour, S. Asgari
{"title":"A new generalization of t-lifting modules","authors":"Y. Talebi, A. R. M. Hamzekolaee, M. Hosseinpour, S. Asgari","doi":"10.22124/JART.2020.16482.1203","DOIUrl":"https://doi.org/10.22124/JART.2020.16482.1203","url":null,"abstract":"In this paper we introduce the concept of $tCC$-modu-les which is a proper generalizationof ($t$-)lifting modules. Let $M$ be a module over a ring $R$.We call $M$ a $tCC$-module(related to $t$-coclosed submodules) provided that for every$t$-coclosed submodule $N$ of $M$, there exists a direct summand $K$ of $M$such that $M=N+K$ and $Ncap Kll K$.We prove that a module with $(D_3)$ property is $tCC$if and only if every direct summand of $M$ is $tCC$. It is also shownthat an amply supplemented module $M$ is $tCC$ if and only if $M$ decomposed to$overline{Z}^2(M)$ and a submodule $L$ of $M$ that both of them are $tCC$.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"8 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48031193","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
2-absorbing delta-primary elements in multiplicative lattices 乘法格中的2-吸收delta主元素
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.11322.1118
J. Nehete, S. Nimbhorkar
{"title":"2-absorbing delta-primary elements in multiplicative lattices","authors":"J. Nehete, S. Nimbhorkar","doi":"10.22124/JART.2019.11322.1118","DOIUrl":"https://doi.org/10.22124/JART.2019.11322.1118","url":null,"abstract":"","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"45-64"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45600791","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
e-lifting modules relative to fully invariant submodules 相对于完全不变子模块的e提升模块
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.11972.1135
F. Alizadeh, M. Hosseinpour, Z. Kamali
{"title":"e-lifting modules relative to fully invariant submodules","authors":"F. Alizadeh, M. Hosseinpour, Z. Kamali","doi":"10.22124/JART.2019.11972.1135","DOIUrl":"https://doi.org/10.22124/JART.2019.11972.1135","url":null,"abstract":"In this paper, we introduce the notion FI-e-lifting modules which is a proper generalization of lifting (e-lifting) modules.Then we give some characterizations and properties of e-lifting and FI-e-lifting modules. We provide a decomposition of any e-lifting modules. It is shown that every finite direct sum of FI-e-lifting modules is FI-e-lifting","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"13-24"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49260213","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
The $ k $-${rm bf{ th}}$ spectral moment of signed complete graphs 有符号完全图的$k$-${rm-bf-{th}$谱矩
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.13670.1150
S. Dalvandi, F. Heydari, M. Maghasedi
{"title":"The $ k $-${rm bf{ th}}$ spectral moment of signed complete graphs","authors":"S. Dalvandi, F. Heydari, M. Maghasedi","doi":"10.22124/JART.2019.13670.1150","DOIUrl":"https://doi.org/10.22124/JART.2019.13670.1150","url":null,"abstract":"Let $Gamma=(G,sigma)$ be a signed graph, where $G$ is the underlying simple graph with at least one edge and $sigma : E(G) longrightarrow lbrace -,+rbrace$ is the sign function on the edges of $G$. In this paper, we study the $ k $-th spectral moment of $(K_n,sigma)$, for a signature $sigma$. Also, we obtain the number of negative cycles in a signed complete graph whose negative edges induce the disjoint union of two distinct complete bipartite graphs.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"35-44"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45338836","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 Class of Subsets of Residuated lattice which induces a Congruence Relation 关于一类导出同余关系的剩余格的子集
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.11333.1119
H. Harizavi
{"title":"On the Class of Subsets of Residuated lattice which induces a Congruence Relation","authors":"H. Harizavi","doi":"10.22124/JART.2019.11333.1119","DOIUrl":"https://doi.org/10.22124/JART.2019.11333.1119","url":null,"abstract":"In this manuscript,  we study the class of special subsets connected with a  subset in a residuated lattice and investigate some related properties. We describe the union of elements of this class. Using the intersection of all special subsets connected with a subset, we give a necessary and sufficient condition for a subset to be a filter.  Finally, by defining some operations, we endow this class with a residuated lattice structure and prove that it is isomorphic to the set of all congruence classes with respect to a filter.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45193308","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
The inverse monoid associated to a group and the semidirect product of groups 与群相关的逆半群与群的半直积
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.11348.1120
N. Ghadbane
{"title":"The inverse monoid associated to a group and the semidirect product of groups","authors":"N. Ghadbane","doi":"10.22124/JART.2019.11348.1120","DOIUrl":"https://doi.org/10.22124/JART.2019.11348.1120","url":null,"abstract":"In this paper, we construct an inverse monoid $Mleft( Gright) $ associatedto a given group $G$ by using the notion of the join of subgroups and then,by applying the left action of monoid $M$ on a semigroup $S$, we form asemigroup $Somega M$ on the set $Stimes M$. The finally result is to buildthe semi direct product of groups associated to the group action on ananother group.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"25-34"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43661191","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
A new Gaussian Fibonacci matrices and its applications 一种新的高斯Fibonacci矩阵及其应用
Journal of Algebra and Related Topics Pub Date : 2019-06-01 DOI: 10.22124/JART.2019.12999.1144
B. Prasad
{"title":"A new Gaussian Fibonacci matrices and its applications","authors":"B. Prasad","doi":"10.22124/JART.2019.12999.1144","DOIUrl":"https://doi.org/10.22124/JART.2019.12999.1144","url":null,"abstract":"In this paper, we introduced a new Gaussian Fibonacci matrix, $G^{n}$ whose elements are Gaussian Fibonacci numbers and we developed a new coding and decoding method followed from this Gaussian Fibonacci matrix, $G^{n}$. We established the relations between the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is $93.33$%.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"7 1","pages":"65-72"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41951787","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: 3
Prime extension dimension of a module 一个模块的素数扩展尺寸
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/JART.2018.11232.1116
T. Duraivel, S. Mangayarcarassy, K. Premkumar
{"title":"Prime extension dimension of a module","authors":"T. Duraivel, S. Mangayarcarassy, K. Premkumar","doi":"10.22124/JART.2018.11232.1116","DOIUrl":"https://doi.org/10.22124/JART.2018.11232.1116","url":null,"abstract":"We have that for a finitely generated module $M$ over a Noetherian ring $A$ any two RPE filtrations of $M$ have same length. We call this length as prime extension dimension of $M$ and denote it as $mr{pe.d}_A(M)$. This dimension measures how far a module is from torsion freeness. We show for every submodule (N) of (M), (mr{pe.d}_A(N)leqmr{pe.d}_A(M)) and (mr{pe.d}_A(N)+mr{pe.d}_A(M/N)geqmr{pe.d}_A(M)). We compute the prime extension dimension of a module using the prime extension dimensions of its primary submodules which occurs in a minimal primary decomposition of (0) in (M).","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"97-106"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42709990","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: 4
Basis of a multicyclic code as an Ideal in F[X_1,...,X_s]/ F[X_1，…，X_s]/中多环码作为理想的基础
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/JART.2018.10977.1110
R. Andriamifidisoa, R. M. Lalasoa, T. Rabeherimanana
{"title":"Basis of a multicyclic code as an Ideal in F[X_1,...,X_s]/","authors":"R. Andriamifidisoa, R. M. Lalasoa, T. Rabeherimanana","doi":"10.22124/JART.2018.10977.1110","DOIUrl":"https://doi.org/10.22124/JART.2018.10977.1110","url":null,"abstract":"First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a basis of a three dimensional cyclic code. We then generalize this construction to a general $s$-dimensional cyclic code.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"63-78"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47742738","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
Quasi-bigraduations of Modules, criteria of generalized analytic independence 模的拟bigraduation，广义分析独立性准则
Journal of Algebra and Related Topics Pub Date : 2018-12-01 DOI: 10.22124/jart.2018.11137.1113
Y. Diagana
{"title":"Quasi-bigraduations of Modules, criteria of generalized analytic independence","authors":"Y. Diagana","doi":"10.22124/jart.2018.11137.1113","DOIUrl":"https://doi.org/10.22124/jart.2018.11137.1113","url":null,"abstract":"Let $mathcal{R}$ be a ring. For a quasi-bigraduation $f=I_{(p,q)}$of ${mathcal{R}} $ we define an $f^{+}-$quasi-bigraduation of an ${%mathcal{R}}$-module ${mathcal{M}}$ by a family $g=(G_{(m,n)})_{(m,n)inleft(mathbb{Z}times mathbb{Z}right) cup {infty }}$ of subgroups of $%{mathcal{M}}$ such that $G_{infty }=(0) $ and $I_{(p,q)}G_{(r,s)}subseteqG_{(p+r,q+s)},$ for all $(p,q)$ and all $(r,s)in left(mathbb{N} timesmathbb{N}right) cup {infty }.$ Here we show that $r$ elements of ${mathcal{R}}$ are $J-$independent oforder $k$ with respect to the $f^{+}$quasi-bigraduation $g$ if and only ifthe following two properties hold: they are $J-$independent of order $k$ with respect to the $^+$%quasi-bigraduation of ring $f_2(I_{(0,0)},I)$ and there exists a relation ofcompatibility between $g$ and $g_{I}$, where $I$ is the sub-$mathcal{A}-$%module of $mathcal{R}$ constructed by these elements. We also show that criteria of $J-$independence of compatiblequasi-bigraduations of module are given in terms of isomorphisms of gradedalgebras.","PeriodicalId":52302,"journal":{"name":"Journal of Algebra and Related Topics","volume":"6 1","pages":"79-96"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45608359","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
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