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Betti numbers for modules of finite length


Authors: Hara Charalambous, E. Graham Evans and Matthew Miller
Journal: Proc. Amer. Math. Soc. 109 (1990), 63-70
MSC: Primary 13H10; Secondary 13H15
DOI: https://doi.org/10.1090/S0002-9939-1990-1013967-1
MathSciNet review: 1013967
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Abstract: Let $ R$ be a Gorenstein local ring of dimension $ d < 5$ and let $ M$ be a module of finite length and finite projective dimension. If $ M$ is not isomorphic to $ R$ modulo a regular sequence, then the Betti numbers of $ M$ satisfy $ {\beta _i}(M) > (_i^d)$ for $ 0 < i < d$, and $ \sum\nolimits_{i = 0}^d {{\beta _i}(M) \geq {2^d} + {2^{d - 1}}} $.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1013967-1
Keywords: Betti numbers, Cohen-Macaulay ring, linkage, Tor-algebra
Article copyright: © Copyright 1990 American Mathematical Society

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