Generalized Regular Sequence and Finiteness of Local Cohomology Modules
Keyword(s):
Let R be a commutative Noetherian local ring, 𝔞 an ideal of R, and M a finitely generated generalized f-module. Let t be a positive integer such that [Formula: see text] and t > dim M - dim M/𝔞M. In this paper, we prove that there exists an ideal 𝔟 ⊇ 𝔞 such that (1) dim M - dim M/𝔟M = t; and (2) the natural homomorphism [Formula: see text] is an isomorphism for all i > t and it is surjective for i = t. Also, we show that if [Formula: see text] is a finite set for all i < t, then there exists an ideal 𝔟 of R such that dim R/𝔟 ≤ 1 and [Formula: see text] for all i < t.
2009 ◽
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pp. 244-250
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2013 ◽
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pp. 1350063
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2019 ◽
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pp. 1950238
2016 ◽
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pp. 1650070
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pp. 935-946
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2009 ◽
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pp. 59-67
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pp. 403-416
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1991 ◽
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pp. 421-429
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