On seminormal monoid rings

Abstract

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 Serre's condition (S-2) and analyze the local cohomology of K[AI]. 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. (c) 2005 Elsevier Inc. All rights reserved.