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VANISHING OF COHOMOLOGY OVER COMPLETE INTERSECTION RINGS

Part of: Commutative algebra: Homological methods Local rings and semilocal rings

Published online by Cambridge University Press:  18 December 2014

ARASH SADEGHI
ARASH SADEGHI*
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran e-mail: sadeghiarash61@gmail.com
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Abstract

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Let R be a complete intersection ring, and let M and N be R-modules. It is shown that the vanishing of ExtiR(M, N) for a certain number of consecutive values of i starting at n forces the complete intersection dimension of M to be at most n–1. We also estimate the complete intersection dimension of M*, the dual of M, in terms of vanishing of cohomology modules, ExtiR(M,N).

MSC classification

Primary: 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 445 - 455
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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