COFINITENESS AND FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES
2009 ◽
Vol 80
(2)
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pp. 244-250
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Keyword(s):
AbstractLet 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.
2019 ◽
Vol 18
(12)
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pp. 1950238
2009 ◽
Vol 79
(1)
◽
pp. 59-67
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2018 ◽
Vol 11
(02)
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pp. 1850019
2015 ◽
Vol 15
(01)
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pp. 1650019
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2016 ◽
Vol 15
(04)
◽
pp. 1650070
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2015 ◽
Vol 22
(spec01)
◽
pp. 935-946
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