The ascending chain condition on principal right ideals for semigroup constructions

IF 0.6 3区数学 Q3 MATHEMATICS

Periodica Mathematica Hungarica Pub Date : 2023-12-14 DOI:10.1007/s10998-023-00570-1

Craig Miller

引用次数: 0

Abstract

We call a semigroup \({\mathcal {R}}\)-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on \({\mathcal {R}}\)-classes. We investigate the behaviour of the property of being \({\mathcal {R}}\text {-noetherian}\) under the following standard semigroup-theoretic constructions: semidirect products, Schützenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck–Reilly extensions and semilattices of semigroups.

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半群构造的主权利理想的升链条件

如果一个半群在主右理想上满足升链条件，或者在\({\mathcal {R}}\) -类上满足升链条件，我们称它为\({\mathcal {R}}\) -noether。研究了在半群的半直积、sch岑伯格积、自由积、Rees矩阵半群、Brandt扩展、Bruck-Reilly扩展和半格等标准半群理论构造下的性质\({\mathcal {R}}\text {-noetherian}\)的行为。

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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来源期刊

Periodica Mathematica Hungarica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.