A monoid S is said to be weakly right coherent if every finitely generated right ideal of S is finitely presented as a right S-act. It is known that S is weakly right coherent if and only if it satisfies the following conditions: S is right ideal Howson, meaning that the intersection of any two finitely generated right ideals of S is finitely generated; and the right annihilator congruences r(a)={(u,v) in S x S | au=av} for each a in S are finitely generated as right congruences.
This talk will introduce basic semigroup theoretic concepts as is necessary before briefly surveying some important coherency-related results. Closure properties of the classes of monoids satisfying each of the above properties will be shared, with details explored for a specific construction. Time permitting, connections with axiomatisation will be discussed.
This talk will in part be based on a paper written with coauthors Craig Miller and Victoria Gould, preprint available at: arXiv:2411.03947.