正则元的一元上的对偶性质

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-04-30 DOI:10.1142/s1005386722000165

C. Hong, H. Kim, N. Kim, T. Kwak, Yang Lee

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引用次数: 1

摘要

本文研究了正则元素上的右对偶性质，给出了具有此性质的环是右DR。首先证明了当给定的环是右DR时，右商环保留了右对偶性质。证明了环上的多项式环[公式:见文]是右DR当且仅当[公式:见文]是可交换的。还证明了对于素数[公式:见文]，在特征[公式:见文]的域[公式:见文]上的有限[公式:见文]群[公式:见文]的群环[公式:见文]当且仅当它是右对偶时是右DR，当[公式:见文]不是[公式:见文]群时存在一个既不是DR又不是对偶的群环[公式:见文]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Duo Property on the Monoid of Regular Elements

We study the right duo property on regular elements, and we say that rings with this property are right DR. It is first shown that the right duo property is preserved by right quotient rings when the given rings are right DR. We prove that the polynomial ring over a ring [Formula: see text] is right DR if and only if [Formula: see text] is commutative. It is also proved that for a prime number [Formula: see text], the group ring [Formula: see text] of a finite [Formula: see text]-group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] is right DR if and only if it is right duo, and that there exists a group ring [Formula: see text] that is neither DR nor duo when [Formula: see text] is not a [Formula: see text]-group.

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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.