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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1129869-9
PII: S 0002-9939(1993)1129869-9
Keywords: Tight closure, test elements, uniform Artin-Rees
Article copyright: © Copyright 1993 American Mathematical Society