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

الأصل · EN

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)∩ mˢ⁻¹=mˢ. We prove that the Poincaré 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.