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International Electronic Journal of Algebra最新文献

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Rota---Baxter operators on $Cur(sl_2(mathbb{C}))$ Rota—$Cur(sl_2(mathbb{C}))$上的Baxter运算符
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-12-13 DOI: 10.24330/ieja.1218727
V. Gubarev, R. Kozlov
{"title":"Rota---Baxter operators on $Cur(sl_2(mathbb{C}))$","authors":"V. Gubarev, R. Kozlov","doi":"10.24330/ieja.1218727","DOIUrl":"https://doi.org/10.24330/ieja.1218727","url":null,"abstract":"We classify all Rota---Baxter operators on the simple Lie conformal algebra $Cur(sl_2(mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang---Baxter equation due to the connection discovered by Y. Hong and C. Bai in 2020.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47383321","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
When do quasi-cyclic codes have $mathbb F_{q^l}$-linear image? 什么时候准循环码有$mathbb F_{q^l}$-线性图像?
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-11-01 DOI: 10.24330/ieja.1198011
R. Nekooei, Z. Pourshafiey
{"title":"When do quasi-cyclic codes have $mathbb F_{q^l}$-linear image?","authors":"R. Nekooei, Z. Pourshafiey","doi":"10.24330/ieja.1198011","DOIUrl":"https://doi.org/10.24330/ieja.1198011","url":null,"abstract":"A length $ml$, index $l$ quasi-cyclic code can be viewed as a cyclic code of length $m$ over the field $mathbb F_{q^l}$ via a basis of the extension $mathbb F_{q^l}/mathbb F_{q}$. \u0000This cyclic code is an additive cyclic code. \u0000In [C. Güneri, F. Özdemir, P. Solé, On the additive cyclic structure of quasi-cyclic codes, Discrete. Math., 341 (2018), 2735-2741], authors characterize \u0000the $(l,m)$ values for one-generator quasi-cyclic codes for which it is \u0000impossible to have an $mathbb F_{q^l}$-linear image for any choice \u0000of the polynomial basis of $mathbb F_{q^l}/mathbb F_{q}$. \u0000But this characterization for some $(l,m)$ \u0000values is very intricate. In this paper, by the use of this characterization, we give a more simple characterization.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48919483","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
Cayley subspace sum graph of vector spaces 向量空间的Cayley子空间和图
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-10-27 DOI: 10.24330/ieja.1195466
G. Kalaimurugan, S. Gopinath, T. Tamizh Chelvam
{"title":"Cayley subspace sum graph of vector spaces","authors":"G. Kalaimurugan, S. Gopinath, T. Tamizh Chelvam","doi":"10.24330/ieja.1195466","DOIUrl":"https://doi.org/10.24330/ieja.1195466","url":null,"abstract":"Let $mathbb{V}$ be a finite dimensional vector space over the field $mathbb{F}$. Let $S(mathbb{V})$ be the set of all subspaces of $mathbb{V}$ and $mathbb{A}subseteq S^*(mathbb{V})=S(mathbb{V})backslash{0}.$ In this paper, we define the Cayley subspace sum graph of $mathbb{V},$ denoted by Cay$(S^*(mathbb{V}),mathbb{A}), $ as the simple undirected graph with vertex set $S^*(mathbb{V})$ and two distinct vertices $X$ and $Y$ are adjacent if $X+Z=Y$ or $Y+Z=X$ for some $Zin mathbb{A}$. Having defined the Cayley subspace sum graph, we study about the connectedness, diameter and girth of several classes of Cayley subspace sum graphs Cay$(S^*(mathbb{V}), mathbb{A})$ for a finite dimensional vector space $mathbb{V}$ and $mathbb{A}subseteq S^*(mathbb{V})=S(mathbb{V})backslash{0}.$","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49534064","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 modules with chain condition on non-small submodules 非小子模块上具有链条件的模块
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-10-27 DOI: 10.24330/ieja.1195509
A. K. Chaturvedi, Nirbhay Kumar
{"title":"On modules with chain condition on non-small submodules","authors":"A. K. Chaturvedi, Nirbhay Kumar","doi":"10.24330/ieja.1195509","DOIUrl":"https://doi.org/10.24330/ieja.1195509","url":null,"abstract":"In 1979, Fleury studied a class of modules with finite spanning dimension and dually a class of modules with ascending chain condition on non-small submodules was studied by Lomp and Ozcan in 2011. In the present work, we explore and investigate some new characterizations and properties of these classes of modules.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46629350","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 Generalized Probability in Finite Commutative Rings 有限交换环上的广义概率
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-08-05 DOI: 10.24330/ieja.1156662
S. Rehman, Muhammad Naveed Shaheryar
{"title":"On Generalized Probability in Finite Commutative Rings","authors":"S. Rehman, Muhammad Naveed Shaheryar","doi":"10.24330/ieja.1156662","DOIUrl":"https://doi.org/10.24330/ieja.1156662","url":null,"abstract":"Let $R$ be a finite commutative ring with unity and $xin R$. We study the probability that the product of two randomly chosen elements (with replacement) of $R$ equals $x$. We denote this probability by $Prob_x (R)$. We determine some bounds for this probability and also obtain some characterizations of finite commutative rings based on this probability. Moreover, we determine the explicit computing formulas for $Prob_x (R)$ when $R=mathbb{Z}_mtimes mathbb{Z}_n$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43726942","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
Planar index and outerplanar index of zero-divisor graphs of commutative rings without identity 无恒等交换环零除数图的平面索引和外平面索引
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-08-01 DOI: 10.24330/ieja.1152714
G. Kalaimurugan, P. Vignesh, M. Afkhami, Z. Barati
{"title":"Planar index and outerplanar index of zero-divisor graphs of commutative rings without identity","authors":"G. Kalaimurugan, P. Vignesh, M. Afkhami, Z. Barati","doi":"10.24330/ieja.1152714","DOIUrl":"https://doi.org/10.24330/ieja.1152714","url":null,"abstract":"Let $R$ be a commutative ring without identity. The zero-divisor graph of $R,$ denoted by $Gamma(R)$ is a graph with vertex set $Z(R)setminus {0}$ which is the set of all nonzero zero-divisor elements of $R,$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0.$ In this paper, we characterize the rings whose zero-divisor graphs are ring graphs and outerplanar graphs. Further, we establish the planar index, ring index and outerplanar index of the zero-divisor graphs of finite commutative rings without identity.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501494","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 structure of matrix polynomial algebras 矩阵多项式代数的结构
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-29 DOI: 10.24330/ieja.1151001
Bertrand Nguefack
{"title":"The structure of matrix polynomial algebras","authors":"Bertrand Nguefack","doi":"10.24330/ieja.1151001","DOIUrl":"https://doi.org/10.24330/ieja.1151001","url":null,"abstract":"This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions \u0000of a coefficient algebra by (elementary) matrix-variables over \u0000 a ground polynomial ring in not necessary commuting variables. \u0000 These matrix subalgebras of full matrix rings over polynomial rings show up \u0000 in noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining a precise lift of the Hilbert Basis Theorem when the \u0000ground ring is either a commutative polynomial ring, a free noncommutative polynomial ring or a skew polynomial ring extension by a free commutative term-ordered monoid. \u0000We equally address the natural but rather delicate question of recognising which matrix polynomial algebras are Cayley-Hamilton algebras, \u0000which are interesting noncommutative algebras arising from the study of $mathrm{Gl}_{n}$-varieties.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48043620","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
Lie structure of the Heisenberg-Weyl algebra Heisenberg—Weyl代数的李结构
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-25 DOI: 10.24330/ieja.1326849
R. Cantuba
{"title":"Lie structure of the Heisenberg-Weyl algebra","authors":"R. Cantuba","doi":"10.24330/ieja.1326849","DOIUrl":"https://doi.org/10.24330/ieja.1326849","url":null,"abstract":"As an associative algebra, the Heisenberg--Weyl algebra $HWeyl$ is generated by two elements $A$, $B$ subject to the relation $AB-BA=1$. As a Lie algebra, however, where the usual commutator serves as Lie bracket, the elements $A$ and $B$ are not able to generate the whole space $HWeyl$. We identify a non-nilpotent but solvable Lie subalgebra $coreLie$ of $HWeyl$, for which, using some facts from the theory of bases for free Lie algebras, we give a presentation by generators and relations. Under this presentation, we show that, for some algebra isomorphism $isoH:HWeylintoHWeyl$, the Lie algebra $HWeyl$ is generated by the generators of $coreLie$, together with their images under $isoH$, and that $HWeyl$ is the sum of $coreLie$, $isoH(coreLie)$ and $lbrak coreLie,isoH(coreLie)rbrak$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42496817","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
Fields whose torsion free parts divisible with trivial Brauer group 无扭转部分可被平凡Brauer群整除的域
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-15 DOI: 10.24330/ieja.1144156
R. Fallah-Moghaddam
{"title":"Fields whose torsion free parts divisible with trivial Brauer group","authors":"R. Fallah-Moghaddam","doi":"10.24330/ieja.1144156","DOIUrl":"https://doi.org/10.24330/ieja.1144156","url":null,"abstract":"Let $F_0$ be an absolutely algebraic field of characteristic $p>0$ and \u0000$kappa$ an infinite cardinal. It is shown that there exists a \u0000field $F$ such that $F^*cong F^*_0oplus(oplus_kappa \u0000mathbb{Q})$ with $Br(F)={0}$. Let $L$ be an algebraic closure \u0000of $F$. Then for any finite subextension $K$ of $L/F$, we have \u0000$K^*cong T(K^*)oplus(oplus_kappa mathbb{Q})$, where $T(K^*)$ \u0000is the group of torsion elements of $K^*$. In addition, \u0000$Br(K)={0}$ and $[K:F]=[T(K^*) cup {0}:F_0]$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43131691","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 solubility of groups with finitely many centralizers 关于具有有限多个中心子的群的溶解度
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-15 DOI: 10.24330/ieja.1144159
I. Lima, Caio Rodrigues
{"title":"On solubility of groups with finitely many centralizers","authors":"I. Lima, Caio Rodrigues","doi":"10.24330/ieja.1144159","DOIUrl":"https://doi.org/10.24330/ieja.1144159","url":null,"abstract":"In this paper we present a new sufficient condition for a solubility criterion in terms of centralizers of elements. This result is a corrigendum of one of Zarrin's results. Furthermore, we extend some of K. Khoramshahi and M. Zarrin's results in the primitive case.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43493133","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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