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

Aberbach, Ian M.

doi:10.1090/S0002-9939-1993-1129869-9

Test elements in excellent rings with an application to the uniform Artin-Rees property
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by Ian M. Aberbach

Proc. Amer. Math. Soc. 118 (1993), 355-363

DOI: https://doi.org/10.1090/S0002-9939-1993-1129869-9

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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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