A formula for the *-core of an ideal

Fouli, Louiza; Vassilev, Janet; Vraciu, Adela

doi:10.1090/S0002-9939-2011-10858-X

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.

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