Free resolutions over short Gorenstein local rings |
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Authors: | In��s Bonacho Dos Anjos Henriques Liana M ?ega |
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Institution: | 1. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588, USA 2. Department of Mathematics and Statistics, University of Missouri, Kansas City, MO, 64110, USA
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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 R (?t) =?1 ? et?+?et 2 ? t 3, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3. |
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