The Koszul property in affine semigroup rings

We investigate the Koszul property for quotients of affine semigroup rings by semigroup ideals. Using a combinatorial and topological. interpretation for the Kloszul property in this context, we recover known results assertin g that certain of these rings are Koszul. In the process, we prove a strong er fact, suggesting a more general definition of Koszul rings, already cons idered by Froberg. This more general definition of Koszulness turns out to be satisfied by all Cohen-Macaulay rings of minimal multiplicity.