Poincare series of compressed local Artinian rings with odd top socle degree

摘要

We define a notion of compressed local Artinian ring that does not require the ring to contain a field. Let (R, m) be a compressed local Artinian ring with odd top socle degree s, at least five, and socle(R) boolean AND ms(-1) = m(s). We prove that the Poincare series of all finitely generated modules over R are rational, sharing a common denominator, and that there is a Golod homomorphism from a complete intersection onto R. (C) 2018 Elsevier Inc. All rights reserved.