The ascending chain condition on principal right ideals for semigroup constructions
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, Sch\"utzenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck-Reilly extensions and semilattices of semigroups.
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