  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.
