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

JOURNAL OF ALGEBRA

卷:505

Article

Kustin, Andrew R.¹  Sega, Liana M.²  Vraciu, Adela¹ 

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[2] Univ Missouri, Dept Math & Stat, Kansas City, MO 64110 USA

关键词: Compressed ring;    Differential graded algebra;    Generic algebra;    Golod homomorphism;    Grassmannian;    Homology algebra of the Koszul complex;    Koszul homology;    Poincare series;    Socle;    Trivial Massey operation;   

DOI  :  10.1016/j.jalgebra.2018.02.034

来源: Elsevier

【 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.

【 授权许可】

Free