{"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}
引用次数: 0
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].
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.
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