A linear function associated to asymptotic prime divisors
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- by Daniel Katz and Eric West PDF
- Proc. Amer. Math. Soc. 132 (2004), 1589-1597 Request permission
Abstract:
Let $R$ be a Noetherian standard ${\mathbb {N}}^{\thinspace d}$-graded ring and $M,N$ finitely generated, ${\mathbb {N}}^{\thinspace d}$-graded $R$-modules. Let $I_{1}, \ldots , I_{s}$ be finitely many homogeneous ideals of $R$. We show that there exist linear functions $f,g : \mathbb {N}^{s} \to \mathbb {N}^{d}$ such that the associated primes over $R_{0}$ of $[\operatorname {Ext}^{i}(N,M/I_{1}^{n_{1}}\cdots I_{s}^{n_{s}}M)]_{m}$ and $[\operatorname {Tor}_{i}(N,M/I_{1}^{n_{1}}\cdots I_{s}^{n_{s}}M)]_{m}$ are stable whenever $m\in {\mathbb {N}}^{\thinspace d}$ satisfies $m\geq f(n_{1},\ldots ,n_{s})$ and $m\geq g(n_{1},\ldots , n_{s})$, respectively.References
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Additional Information
- Daniel Katz
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- Email: dlk@math.ukans.edu
- Eric West
- Affiliation: Department of Mathematics and Computer Science, Benedictine College, Atchison, Kansas 66002
- Email: ewest@benedictine.edu
- Received by editor(s): April 8, 2002
- Received by editor(s) in revised form: February 13, 2003
- Published electronically: October 21, 2003
- Communicated by: Bernd Ulrich
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1589-1597
- MSC (2000): Primary 13A02, 13A15, 13A30, 13E05
- DOI: https://doi.org/10.1090/S0002-9939-03-07282-4
- MathSciNet review: 2051118