On seminormal monoid rings

Given a seminormal affine monoid M we consider several monoid properties of M and their connections to ring properties of the associated affine monoid ring K[M] over a field K. We characterize when K[M] satisfies Serreʹs condition (S2) and analyze the local cohomology of K[M]. As an application we present criteria which imply that K[M] is Cohen–Macaulay and we give lower bounds for the depth of K[M]. Finally, the seminormality of an arbitrary affine monoid M is studied with characteristic p methods.