Coherency and constructions for monoids
arXiv:1906.05515
Abstract
A monoid is right coherent if every finitely generated subact of every finitely presented right -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 to be finitely generated.