Asymptotic prime ideals related to derived functors
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- by Leif Melkersson and Peter Schenzel
- Proc. Amer. Math. Soc. 117 (1993), 935-938
- DOI: https://doi.org/10.1090/S0002-9939-1993-1124148-8
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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
- M. Brodmann, Asymptotic stability of $\textrm {Ass}(M/I^{n}M)$, Proc. Amer. Math. Soc. 74 (1979), no. 1, 16–18. MR 521865, DOI 10.1090/S0002-9939-1979-0521865-8
- D. Kirby, Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford Ser. (2) 24 (1973), 47–57. MR 316446, DOI 10.1093/qmath/24.1.47
- I. G. Macdonald, Secondary representation of modules over a commutative ring, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971 & Convegno di Geometria, INDAM, Rome, 1972) Academic Press, London, 1973, pp. 23–43. MR 0342506
- Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
- Leif Melkersson, On asymptotic stability for sets of prime ideals connected with the powers of an ideal, Math. Proc. Cambridge Philos. Soc. 107 (1990), no. 2, 267–271. MR 1027779, DOI 10.1017/S0305004100068535
- R. Y. Sharp, Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. (2) 34 (1986), no. 2, 212–218. MR 856506, DOI 10.1112/jlms/s2-34.2.212
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 935-938
- MSC: Primary 13E05; Secondary 13A02, 13A30, 13E10
- DOI: https://doi.org/10.1090/S0002-9939-1993-1124148-8
- MathSciNet review: 1124148