Semigroups for which every right congruence of finite index is finitely generated
Craig J. Miller · Monatshefte für Mathematik · 2020
Abstract We call a semigroupSf-noetherian if every right congruence of finite index onSis finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.