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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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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}.
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참고문헌 (9)
참고문헌 신청
K. Khashyarmanesh / 2001 / Asymptotic stability of AttR TorR₁(R/aⁿ,A) / Proc. Edinb. Math. Soc 44 (3) : 479 ~ 483
K. Khashyarmanesh / 2006 / On the finiteness properties of ?i (AssR ExtⁿR (R/ai ,M) / Comm. Algebra 34 (2) : 779 ~ 784
K. Khashyarmanesh / 2008 / Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules / Manuscripta Math 125 : 345 ~ 352
L. Melkersson / 1993 / Asymptotic prime ideals related to derived functors / Proc. Amer. Math. Soc 117 (4) : 935 ~ 938
M. Brodmann / 1979 / Asymptotic stability of AssRM/IⁿM / Proc. Amer. Math. Soc 74 (1) : 16 ~ 18
K. Khashyarmanesh / 2006 / On the finiteness properties of ?i (AssR ExtⁿR (R/ai ,M) / Comm. Algebra 34 (2) : 779 ~ 784
K. Khashyarmanesh / 2008 / Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules / Manuscripta Math 125 : 345 ~ 352
L. Melkersson / 1993 / Asymptotic prime ideals related to derived functors / Proc. Amer. Math. Soc 117 (4) : 935 ~ 938
M. Brodmann / 1979 / Asymptotic stability of AssRM/IⁿM / Proc. Amer. Math. Soc 74 (1) : 16 ~ 18
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