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arXiv · 2302.01847

The ascending chain condition on principal right ideals for semigroup constructions

Craig Miller
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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 $\mathcal{R}$-noetherian under the following standard semigroup-theoretic constructions: semidirect products, Sch\"utzenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck-Reilly extensions and semilattices of semigroups.

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Craig Miller. 2023-02-03. The ascending chain condition on principal right ideals for semigroup constructions. https://arxiv.org/abs/2302.01847

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