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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the surjectivity criterion for Buchsbaum modules


Author: Shiro Goto
Journal: Proc. Amer. Math. Soc. 108 (1990), 641-646
MSC: Primary 13H10; Secondary 13D03
MathSciNet review: 998734
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Abstract: Let $ R$ be a Cohen-Macaulay local ring with maximal ideal $ m$ and suppose that $ \dim R \geq 2$. Then $ R$ is regular if (and only if) for any Buchsbaum $ R$-module $ M$ and for any integer $ i,i \ne {\dim _R}M$, the canonical map $ {\text{Ext}}_R^i\left( {R/m,M} \right) \to H_m^i\left( M \right): = \lim_{\substack{\to\\ n}} \mathrm{Ext}_R^i \left(R/m^n, M \right)$ is surjective. The hypothesis that $ R$ is Cohen-Macaulay is not superfluous. Two examples are given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0998734-7
PII: S 0002-9939(1990)0998734-7
Article copyright: © Copyright 1990 American Mathematical Society