Coherency and Constructions for Monoids

Abstract

A monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard algebraic and semigroup theoretic constructions: subsemigroups, homomorphic images, direct products, Rees matrix semigroups, including Brandt semigroups, and Bruck–Reilly extensions. We also investigate the relationship with the property of being weakly right noetherian, which requires all right ideals of S to be finitely generated.

Chain conditions on (Rees) congruences of S-acts

“…Right noetherian semigroups were further studied by Kozhukhov in [7]. According to [2,4], a monoid S is called weakly right noetherian if every right ideal is finitely generated, and it is said to be right noetherian if every right congruence is finitely generated. Later on, some connections between noetherian properties of a monoid and coherency were investigated.…”