## Osaka Journal of Mathematics

### A length characterization of $*$-spread

#### Abstract

The $*$-spread of an ideal is defined as the minimal number of generators of an ideal which is minimal with respect to having the same tight closure as the original ideal. We prove an asymptotic length formula for the $*$-spread.

#### Article information

Source
Osaka J. Math. Volume 45, Number 2 (2008), 445-456.

Dates
First available in Project Euclid: 15 July 2008

https://projecteuclid.org/euclid.ojm/1216151108

Mathematical Reviews number (MathSciNet)
MR2441949

Zentralblatt MATH identifier
1145.13002

#### Citation

Epstein, Neil; Vraciu, Adela. A length characterization of $*$-spread. Osaka J. Math. 45 (2008), no. 2, 445--456.https://projecteuclid.org/euclid.ojm/1216151108

#### References

• I.M. Aberbach: Extension of weakly and strongly F-regular rings by flat maps, J. Algebra 241 (2001), 799--807.
• N.M. Epstein: A tight closure analogue of analytic spread, Math. Proc. Cambridge Philos. Soc. 139 (2005), 371--383.
• M. Hochster and C. Huneke: Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31--116.
• C. Lech: On the associativity formula for multiplicities, Ark. Mat. 3 (1957), 301--314.
• P. Monsky: The Hilbert-Kunz function, Math. Ann. 263 (1983), 43--49.
• D.G. Northcott and D. Rees: Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145--158.
• A. Vraciu: $\ast$-independence and special tight closure, J. Algebra 249 (2002), 544--565.