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- Title
Free resolutions over short Gorenstein local rings.
- Authors
Henriques, Inês Bonacho Dos Anjos; Şega, Liana M.
- Abstract
Let R be a local ring with maximal ideal $${\mathfrak{m}}$$ admitting a non-zero element $${a\in\mathfrak{m}}$$ for which the ideal (0 : a) is isomorphic to R/ aR. We study minimal free resolutions of finitely generated R-modules M, with particular attention to the case when $${\mathfrak{m}^4=0}$$. Let e denote the minimal number of generators of $${\mathfrak{m}}$$. If R is Gorenstein with $${\mathfrak{m}^4=0}$$ and e ≥ 3, we show that $${{\rm P}_{M}^{R}(t)}$$ is rational with denominator H(− t) = 1 − et + et − t, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3.
- Subjects
GORENSTEIN rings; FREE resolutions (Algebra); MODULES (Algebra); GENERATORS of groups; LOCAL rings (Algebra)
- Publication
Mathematische Zeitschrift, 2011, Vol 267, Issue 3/4, p645
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-009-0639-z