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Test elements in excellent rings with an application to the uniform Artin-Rees property

Author: Ian M. Aberbach
Journal: Proc. Amer. Math. Soc. 118 (1993), 355-363
MSC: Primary 13A35; Secondary 13D25, 13F40
MathSciNet review: 1129869
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Abstract: Working in positive prime characteristic throughout, we show that excellent rings of dimension $ 2$ or smaller have completely stable test elements and use this to show that excellent domains of dimension $ 3$ have the uniform Artin-Rees property.

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Keywords: Tight closure, test elements, uniform Artin-Rees
Article copyright: © Copyright 1993 American Mathematical Society

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