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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic prime ideals related to derived functors


Authors: Leif Melkersson and Peter Schenzel
Journal: Proc. Amer. Math. Soc. 117 (1993), 935-938
MSC: Primary 13E05; Secondary 13A02, 13A30, 13E10
MathSciNet review: 1124148
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Abstract: Let $ R$ be a commutative noetherian ring. Let $ N$ (resp. $ A$) denote a noetherian (resp. artinian) $ R$-module and $ I$ an ideal of $ \left[ R \right]$. It is shown that for each integer $ i$ the sets of prime ideals $ {\operatorname{Ass} _R}\operatorname{Tor} _i^R(R/{I^n},N)$ and $ {\operatorname{Att} _R}\operatorname{Ext} _R^i(R/{I^n},A),\;n = 1,2, \ldots $, become for $ n$ large independent of $ n$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1124148-8
PII: S 0002-9939(1993)1124148-8
Keywords: Associated prime, attached prime, asymptotic prime, Tor, Ext, Rees ring
Article copyright: © Copyright 1993 American Mathematical Society