Betti numbers for modules of finite length

Charalambous, Hara; Evans, E. Graham; Miller, Matthew

doi:10.1090/S0002-9939-1990-1013967-1

Betti numbers for modules of finite length
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by Hara Charalambous, E. Graham Evans and Matthew Miller PDF

Proc. Amer. Math. Soc. 109 (1990), 63-70 Request permission

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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