The ascending chain condition on principal right ideals for semigroup constructions
Craig J. Miller · Periodica Mathematica Hungarica · 2023
Abstract We call a semigroup $${\mathcal {R}}$$ R -noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on $${\mathcal {R}}$$ R -classes. We investigate the behaviour of the property of being $${\mathcal {R}}\text {-noetherian}$$ 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.