Test ideals in quotients

of -finite regular local rings

Author:
Janet Cowden Vassilev

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4041-4051

MSC (1991):
Primary 13A35

DOI:
https://doi.org/10.1090/S0002-9947-98-02128-X

MathSciNet review:
1458336

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an -finite regular local ring and an ideal contained in . Let . Fedder proved that is -pure if and only if . We have noted a new proof for his criterion, along with showing that , where is the pullback of the test ideal for . Combining the the -purity criterion and the above result we see that if is -pure then is also -pure. In fact, we can form a filtration of , that stabilizes such that each is -pure and its test ideal is . To find examples of these filtrations we have made explicit calculations of test ideals in the following setting: Let , where is either a polynomial or a power series ring and is generated by monomials and the are regular. Set . Then .

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Additional Information

**Janet Cowden Vassilev**

Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024

Address at time of publication:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, Virginia 23284

Email:
jcvassil@saturn.vcu.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-02128-X

Keywords:
Tight closure,
test element,
$F$-finite,
$F$-pure

Received by editor(s):
November 4, 1996

Additional Notes:
I would like to express my appreciation to Purdue University for hosting me during the time that I completed these results. I also thank Craig Huneke for many helpful conversations.

Article copyright:
© Copyright 1998
American Mathematical Society