Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC