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COFINITENESS AND FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Part of: Commutative algebra: Homological methods

Published online by Cambridge University Press:  23 July 2009

LIZHONG CHU
LIZHONG CHU*
Affiliation:
Department of Mathematics, Suzhou University, 215006, Jiangsu, PR China (email: [email protected])
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Abstract

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Let I be an ideal of a commutative Noetherian local ring R, and M and N two finitely generated modules. Let t be a positive integer. We mainly prove that (i) if HIi(M,N) is Artinian for all i<t, then HIi(M,N) is I-cofinite for all i<t and Hom(R/I,HIt(M,N)) is finitely generated; (ii) if d=pd(M)<∞ and dim N=n<∞, then HId+n(M,N) is I-cofinite. We also prove that if M is a nonzero cyclic R-module, then HIi(N) is finitely generated for all i<t if and only if HIi(M,N) is finitely generated for all i<t.

Keywords

local cohomologygeneralized local cohomologycofiniteArtinian

MSC classification

Secondary: 13D45: Local cohomology
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 244 - 250
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

Supported by the National Natural Science Foundation (No. 10771152) of China, by the Research Foundation (No. Q4107805) of Suzhou University and by the Research Foundation of Pre-research Project (No. Q3107852) of Suzhou University.

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