幂和正则元素的二重性质

Pub Date : 2022-03-20 DOI:10.1142/s1005386723000032

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

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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。

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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].

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