ON FINITENESS PROPERTIES ON ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES AND EXT-MODULES
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초록
Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim R H i I (M) ≤ k for ∀i < t, then [수식] for ∀j ≤ t and ∀n > 0. This shows that [수식] is a finite set for ∀i ≤ t. Also, we prove that [수식] if x 1 ,x 2 ,...,x r is M-sequences in dimension > k and n 1 ,n 2 ,...,n r are some positive integers. Here, for a subset T of Spec(R), set T ≥i = {p ∈ T | dimR/p ≥ i}.
Abstract
Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim R H i I (M) ≤ k for ∀i < t, then [수식] for ∀j ≤ t and ∀n > 0. This shows that [수식] is a finite set for ∀i ≤ t. Also, we prove that [수식] if x 1 ,x 2 ,...,x r is M-sequences in dimension > k and n 1 ,n 2 ,...,n r are some positive integers. Here, for a subset T of Spec(R), set T ≥i = {p ∈ T | dimR/p ≥ i}.
참고문헌 (9)
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