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• W2079889506 abstract "Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M an R-module. The purpose of this paper is to show that if M is finitely generated and dim M/𝔞M > 1, then the R-module ∪{N|N is a submodule of [Formula: see text] and dim N ≤ 1} is 𝔞-cominimax and for some x ∈ R is Rx + 𝔞-cofinite, where t ≔ gdepth (𝔞, M). For any nonnegative integer l, it is also shown that if R is semi-local and M is weakly Laskerian, then for any submodule N of [Formula: see text] with dim N ≤ 1 the associated primes of [Formula: see text] are finite, whenever [Formula: see text] for all i < l. Finally, we show that if (R, 𝔪) is local, M is finitely generated, [Formula: see text] for all i < l, and [Formula: see text] then there exists a generalized regular sequence x 1 , …, x l ∈ 𝔞 on M such that [Formula: see text]." @default.
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• W2079889506 date "2010-04-01" @default.
• W2079889506 modified "2023-10-07" @default.
• W2079889506 title "FINITENESS PROPERTIES OF LOCAL COHOMOLOGY MODULES AND GENERALIZED REGULAR SEQUENCES" @default.
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• W2079889506 doi "https://doi.org/10.1142/s0219498810003951" @default.
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