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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$.

References [Enhancements On Off] (What's this?)

  • [1] M. Brodmann, Asymptotic stability of $ \operatorname{Ass} (M/{I^n}M)$, Proc. Amer. Math. Soc. 74 (1979), 16-18. MR 521865 (80c:13012)
  • [2] D. Kirby, Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford (2) 24 (1973), 47-57. MR 0316446 (47:4993)
  • [3] I. G. Macdonald, Secondary representations of modules over a commutative ring, Sympos. Math., vol. 11, Academic Press, London and New York, 1973, pp. 23-43. MR 0342506 (49:7252)
  • [4] H. Matsumura, Commmutative ring theory, Cambridge Univ. Press, Cambridge, 1986. MR 879273 (88h:13001)
  • [5] L. Melkersson, On asymptotic stability for sets of prime ideals connected with the powers of an ideal, Math. Proc. Cambridge Philos. Soc. 107 (1990), 267-271. MR 1027779 (90k:13014)
  • [6] R. Y. Sharp, Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. (2) 34 (1986), 212-218. MR 856506 (87i:13007)

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Keywords: Associated prime, attached prime, asymptotic prime, Tor, Ext, Rees ring
Article copyright: © Copyright 1993 American Mathematical Society

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