幂和正则元素的二重性质

IF 0.4 4区数学 Q4 MATHEMATICS Algebra Colloquium Pub Date : 2022-03-20 DOI:10.1142/s1005386723000032

T. Kwak, Yang Lee, Zhelin Piao, Yeonsook Seo

{"title":"幂和正则元素的二重性质","authors":"T. Kwak, Yang Lee, Zhelin Piao, Yeonsook Seo","doi":"10.1142/s1005386723000032","DOIUrl":null,"url":null,"abstract":"The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements. Such rings shall be called right exp-DR. We investigate the structures of group rings, right quotient rings, matrix rings and (skew) polynomial rings, through the study of right exp-DR rings. In addition, we provide a method of constructing finite non-abelian [Formula: see text]-groups for any prime [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"58 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Duo Property Applied to Powers and Regular Elements\",\"authors\":\"T. Kwak, Yang Lee, Zhelin Piao, Yeonsook Seo\",\"doi\":\"10.1142/s1005386723000032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements. Such rings shall be called right exp-DR. We investigate the structures of group rings, right quotient rings, matrix rings and (skew) polynomial rings, through the study of right exp-DR rings. In addition, we provide a method of constructing finite non-abelian [Formula: see text]-groups for any prime [Formula: see text].\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":\"58 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386723000032\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386723000032","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文的目的是研究一类环，在这些环中，对幂元和所有正则元的单阵应用了右对偶性质。这种环应称为右exp-DR。通过对右exp-DR环的研究，研究了群环、右商环、矩阵环和(斜)多项式环的结构。此外，我们还提供了一种构造任意素数的有限非阿贝尔群的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Duo Property Applied to Powers and Regular Elements

The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements. Such rings shall be called right exp-DR. We investigate the structures of group rings, right quotient rings, matrix rings and (skew) polynomial rings, through the study of right exp-DR rings. In addition, we provide a method of constructing finite non-abelian [Formula: see text]-groups for any prime [Formula: see text].

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.

期刊最新文献

A New Young Wall Realization of B ( λ ) and B ( ∞ ) The Comaximal Graphs of Noncommutative Rings Left-Symmetric Superalgebra Structures on an Infinite-Dimensional Lie Superalgebra On ϕ - ( n,N ) -ideals of Commutative Rings McKay Matrices for Pointed Rank One Hopf Algebras of Nilpotent Type