Some properties of projective modules over discrete Hodge algebras

✍ Scribed by Andreas Wiemers

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 747 KB
• Volume: 150
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(05)80039-0

✦ Synopsis

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.ring 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 (i) P has the cancellation property, i.e., for every B-module Q B(DP~_B@Q implies P~Q.