A formula for the $*$-core of an ideal
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- by Louiza Fouli, Janet C. Vassilev and Adela N. Vraciu
- Proc. Amer. Math. Soc. 139 (2011), 4235-4245
- DOI: https://doi.org/10.1090/S0002-9939-2011-10858-X
- Published electronically: April 27, 2011
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Abstract:
Expanding on the 2010 work of Fouli and Vassilev, we determine a formula for the $*\textrm {-}\textrm {core}$ of an ideal in two different settings: (1) in a Cohen–Macaulay local ring of characteristic $p>0$, with perfect residue field and test ideal of depth at least two, where the ideal has a minimal $*$-reduction that is a parameter ideal, and (2) in a normal local domain of characteristic $p>0$, with perfect residue field and $\mathfrak {m}$-primary test ideal, where the ideal is a sufficiently high Frobenius power of an ideal. We also exhibit some examples where our formula fails if our hypotheses are not met.References
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Bibliographic Information
- Louiza Fouli
- Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
- MR Author ID: 835733
- Email: lfouli@math.nmsu.edu
- Janet C. Vassilev
- Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
- Email: jvassil@math.unm.edu
- Adela N. Vraciu
- Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
- MR Author ID: 663506
- Email: vraciu@math.sc.edu
- Received by editor(s): October 23, 2009
- Received by editor(s) in revised form: October 22, 2010
- Published electronically: April 27, 2011
- Additional Notes: The second author was partly supported by the NSA grant H98230-09-1-0057
- Communicated by: Bernd Ulrich
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 4235-4245
- MSC (2010): Primary 13A30, 13A35, 13B22
- DOI: https://doi.org/10.1090/S0002-9939-2011-10858-X
- MathSciNet review: 2823069