Asymptotic prime ideals related to derived functors

Melkersson, Leif; Schenzel, Peter

doi:10.1090/S0002-9939-1993-1124148-8

Asymptotic prime ideals related to derived functors
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by Leif Melkersson and Peter Schenzel PDF

Proc. Amer. Math. Soc. 117 (1993), 935-938 Request permission

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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