On the regularity of $p$-Borel ideals
HTML articles powered by AMS MathViewer
- by Jürgen Herzog and Dorin Popescu PDF
- Proc. Amer. Math. Soc. 129 (2001), 2563-2570 Request permission
Abstract:
In this paper we prove Pardue’s conjecture on the regularity of principal $p$-Borel ideals. As a consequence we obtain an upper bound for the regularity of general $p$-Borel ideals.References
- Annetta Aramova and Jürgen Herzog, $p$-Borel principal ideals, Illinois J. Math. 41 (1997), no. 1, 103–121. MR 1433189
- David Bayer and Michael Stillman, A criterion for detecting $m$-regularity, Invent. Math. 87 (1987), no. 1, 1–11. MR 862710, DOI 10.1007/BF01389151
- Shalom Eliahou and Michel Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), no. 1, 1–25. MR 1037391, DOI 10.1016/0021-8693(90)90237-I
- David Eisenbud, Alyson Reeves, and Burt Totaro, Initial ideals, Veronese subrings, and rates of algebras, Adv. Math. 109 (1994), no. 2, 168–187. MR 1304751, DOI 10.1006/aima.1994.1085
- V. Ene, G. Pfister and D. Popescu, Betti numbers for $p$-stable ideals, Comm. Algebra 28 (2000), 1515–1531.
- K. Pardue, Nonstandard Borel-fixed ideals, Dissertation, Brandeis University, 1994.
Additional Information
- Jürgen Herzog
- Affiliation: FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany
- MR Author ID: 189999
- Email: juergen.herzog@uni-essen.de
- Dorin Popescu
- Affiliation: Institute of Mathematics, University of Bucharest, P.O. Box 1-764, Bucharest 70700, Romania
- Email: dorin@stoilow.imar.ro
- Received by editor(s): October 12, 1999
- Received by editor(s) in revised form: January 24, 2000
- Published electronically: February 9, 2001
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2563-2570
- MSC (1991): Primary 13P10; Secondary 13D02, 13C13
- DOI: https://doi.org/10.1090/S0002-9939-01-05840-3
- MathSciNet review: 1838378