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arXiv · 1607.05594

Poincar\'e series of compressed local Artinian rings with odd top socle degree

Andrew R. Kustin·Liana M. Sega·Adela Vraciu
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Abstract

We define a notion of compressed local Artinian ring that does not require the ring to contain a field. Let $(R,\mathfrak m)$ be a compressed local Artinian ring with odd top socle degree $s$, at least five, and $\operatorname{socle}(R)\cap \mathfrak m^{s-1}=\mathfrak m^s$. We prove that the Poincar\'e 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 $R$.

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Andrew R. Kustin, Liana M. Sega, Adela Vraciu. 2016-07-19. Poincar\'e series of compressed local Artinian rings with odd top socle degree. https://arxiv.org/abs/1607.05594

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