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The ascending chain condition on principal right ideals for semigroup constructions

2023/02/03 by D. Craig Miller, Miller, Craig
Mathematics · Computer Science · #Rings, Modules, and Algebras #semigroups and automata theory #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2302.01847

Abstract

We call a semigroup R-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on R-classes. We investigate the behaviour of the property of being R-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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