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International Electronic Journal of Algebra最新文献

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Annihilator conditions with generalized skew derivations and Lie ideals of prime rings 广义偏导的湮灭子条件及素环的李理想
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-14 DOI: 10.24330/ieja.1143810
V. De Filippis, N. Rehman, G. Scudo
{"title":"Annihilator conditions with generalized skew derivations and Lie ideals of prime rings","authors":"V. De Filippis, N. Rehman, G. Scudo","doi":"10.24330/ieja.1143810","DOIUrl":"https://doi.org/10.24330/ieja.1143810","url":null,"abstract":"Let $R$ be a prime ring, $Q_r$ its right Martindale quotient ring, $L$ a non-central Lie ideal of $R$, $ngeq 1$ a fixed integer, $F$ and $G$ two generalized skew derivations of $R$ with the same associated automorphism, $pin R$ a fixed element. If $pbigl(F(x)F(y)-G(y)xbigr)^n=0$, for any $x,y in L$, then there exist $a,cin Q_r$ such that $F(x)=ax$ and $G(x)=cx$, for any $xin R$, with $pa=pc=0$, unless when $R$ satisfies the standard polynomial identity $s_4(x_1,ldots,x_4)$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41729569","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
Strongly EP elements and the solutions of equations in rings 强EP元与环上方程的解
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-14 DOI: 10.24330/ieja.1143740
Yue Sui, Yimin Huang, Junchao Wei
{"title":"Strongly EP elements and the solutions of equations in rings","authors":"Yue Sui, Yimin Huang, Junchao Wei","doi":"10.24330/ieja.1143740","DOIUrl":"https://doi.org/10.24330/ieja.1143740","url":null,"abstract":"In this paper, we present many new characterizations of strongly EP elements in rings with involution. We especially investigate the strongly EP elements by constructing certain equations and considering the solutions of equations, revealing the existence of solutions of certain equations and the general solutions of some binary equations that play a role in characterizing strongly EP elements. Proofs of relevant conclusions are also given.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46356851","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
Ideals in the center of symmetric algebras 对称代数中心的理想
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-07-04 DOI: 10.24330/ieja.1295669
Sofia Brenner, B. Kulshammer
{"title":"Ideals in the center of symmetric algebras","authors":"Sofia Brenner, B. Kulshammer","doi":"10.24330/ieja.1295669","DOIUrl":"https://doi.org/10.24330/ieja.1295669","url":null,"abstract":"We study symmetric algebras $A$ over a field $F$ in which the Jacobson radical of the center of $A$, the socle of the center of $A$ or the Reynolds ideal of $A$ are ideals.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44067087","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
Deformations and Extensions of BiHom-alternative algebras BiHom替换代数的变形与扩张
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-06-15 DOI: 10.24330/ieja.1260492
T. Chtioui, S. Mabrouk, A. Makhlouf
{"title":"Deformations and Extensions of BiHom-alternative algebras","authors":"T. Chtioui, S. Mabrouk, A. Makhlouf","doi":"10.24330/ieja.1260492","DOIUrl":"https://doi.org/10.24330/ieja.1260492","url":null,"abstract":"The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and \u0000Hom-alternative algebras, their structure is defined with two \u0000commuting multiplicative linear maps. We study cohomology and \u0000one-parameter formal deformation theory of left BiHom-alternative \u0000algebras. Moreover, we study central and $T_theta$-extensions of \u0000BiHom-alternative algebras and their relationship with \u0000cohomology. \u0000Finally, we investigate generalized derivations and give some relevant results.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48689183","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
Applications of reduced and coreduced modules I 约化模和协约模的应用
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-05-26 DOI: 10.24330/ieja.1299587
D. Ssevviiri
{"title":"Applications of reduced and coreduced modules I","authors":"D. Ssevviiri","doi":"10.24330/ieja.1299587","DOIUrl":"https://doi.org/10.24330/ieja.1299587","url":null,"abstract":"This is the first in a series of papers highlighting the applications of reduced and coreduced modules. Let $R$ be a commutative unital ring and $I$ be an ideal of $R$. We show that $I$-reduced $R$-modules and $I$-coreduced $R$-modules provide a setting in which the Matlis-Greenless-May (MGM) Equivalence and the Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist in the derived category setting. We realise the $I$-torsion and the $I$-adic completion functors as representable functors and under suitable conditions compute natural transformations between them and other functors.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48204020","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
When Does a Quotient Ring of a PID Have the Cancellation Property? 什么时候PID的商环具有消去性?
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-04-12 DOI: 10.24330/ieja.1102363
G. Chang, J. Oh
{"title":"When Does a Quotient Ring of a PID Have the Cancellation Property?","authors":"G. Chang, J. Oh","doi":"10.24330/ieja.1102363","DOIUrl":"https://doi.org/10.24330/ieja.1102363","url":null,"abstract":". An ideal I of a commutative ring is called a cancellation ideal if IB = IC implies B = C for all ideals B and C . Let D be a principal ideal domain (PID), a,b ∈ D be nonzero elements with a (cid:45) b , ( a,b ) D = dD for some d ∈ D , D a = D/aD be the quotient ring of D modulo aD , and bD a = ( a,b ) D/aD ; so bD a is a nonzero commutative ring. In this paper, we show that the following three properties are equivalent: (i) ad is a prime element and a (cid:45) d 2 , (ii) every nonzero ideal of bD a is a cancellation ideal, and (iii) bD a is a field.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45563825","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 (quasi-)morphic property of skew polynomial rings 关于偏斜多项式环的（拟）纯性质
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-04-12 DOI: 10.24330/ieja.1102387
N. Dehghani
{"title":"On (quasi-)morphic property of skew polynomial rings","authors":"N. Dehghani","doi":"10.24330/ieja.1102387","DOIUrl":"https://doi.org/10.24330/ieja.1102387","url":null,"abstract":". The main objective of this paper is to study (quasi-)morphic property of skew polynomial rings. Let R be a ring, σ be a ring homomorphism on R and n ≥ 1. We show that R inherits the quasi-morphic property from R [ x ; σ ] / ( x n +1 ). It is also proved that the morphic property over R [ x ; σ ] / ( x n +1 ) implies that R is a regular ring. Moreover, we characterize a unit-regular ring R via the morphic property of R [ x ; σ ] / ( x n +1 ). We also investigate the relationship between strongly regular rings and centrally morphic rings. For instance, we show that for a domain R , R [ x ; σ ] / ( x n +1 ) is (left) centrally morphic if and only if R is a division ring and σ ( r ) = u − 1 ru for some u ∈ R . Examples which delimit and illustrate our results are provided.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48213498","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
The effect of $S$-accr on intermediate rings between certain pairs of rings $S$-accr对某些环对之间的中间环的影响
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-04-01 DOI: 10.24330/ieja.1096895
S. Visweswaran
{"title":"The effect of $S$-accr on intermediate rings between certain pairs of rings","authors":"S. Visweswaran","doi":"10.24330/ieja.1096895","DOIUrl":"https://doi.org/10.24330/ieja.1096895","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41638157","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
Graded S-1-absorbing prime submodules in graded multiplication modules 梯度乘法模中的梯度s -1吸收素子模
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-03-02 DOI: 10.24330/ieja.1081701
F. Farzalipour, P. Ghiasvand
{"title":"Graded S-1-absorbing prime submodules in graded multiplication modules","authors":"F. Farzalipour, P. Ghiasvand","doi":"10.24330/ieja.1081701","DOIUrl":"https://doi.org/10.24330/ieja.1081701","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46034183","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
Wedderburn decomposition of a semisimple group algebra $mathbb{F}_qG$ from a subalgebra of factor group of $G$ 由因子群$G$的子代数得到半单群代数$mathbb{F}_qG$的Wedderburn分解
IF 0.6
International Electronic Journal of Algebra Pub Date : 2022-02-22 DOI: 10.24330/ieja.1077582
Gaurav Mittal, R. Sharma
{"title":"Wedderburn decomposition of a semisimple group algebra $mathbb{F}_qG$ from a subalgebra of factor group of $G$","authors":"Gaurav Mittal, R. Sharma","doi":"10.24330/ieja.1077582","DOIUrl":"https://doi.org/10.24330/ieja.1077582","url":null,"abstract":"","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44923032","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
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