Some properties of projective modules over discrete Hodge algebras

Abstract

All rings in this paper are assumed to be commutative with 1 and all modules finitely generated. Let B be a discrete Hodge algebra over a.r ing A. By definition this means that B=R/I where R=A[XI ..... X,,] and I is an ideal in R generated by monomials. T. Vorst showed in 1-12] that thebehavior of projective modules over such B is very similar to the case of an ordinary polynomial ring in the following sense: If all projective modules over any polynomial ring with ground ring A are, extended from A, then every projective module over a discrete Hodge algebra over A is extended from A. Let B be a discrete Hodge algebra over a Noetherian ring A and P a projective module over B. S. Mandal proved in [7] that if rank P~> dim B/> dim A + 1 then