On seminormal monoid rings

Details On seminormal monoid rings On seminormal monoid rings

2005-06-12

arxiv.org/abs/math/0506221v1

J. Algebra 302, No. 1, 361-386 (2006)

Mathematics

Commutative Algebra

23 pages

Scientific paper

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[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.

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