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ℚ-Gorenstein splinter rings of characteristic p are F-regular

Published online by Cambridge University Press:  01 September 1999

ANURAG K. SINGH
ANURAG K. SINGH
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, U.S.A., e-mail: [email protected] Present address: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, U.S.A.
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Abstract

A Noetherian integral domain R is said to be a splinter if it is a direct summand, as an R-module, of every module-finite extension ring (see [Ma]). In the case that R contains the field of rational numbers, it is easily seen that R is splinter if and only if it is a normal ring, but the notion is more subtle for rings of characteristic p>0. It is known that F-regular rings of characteristic p are splinters and Hochster and Huneke showed that the converse is true for locally excellent Gorenstein rings [HH4]. In this paper we extend their result by showing that ℚ-Gorenstein splinters are F-regular. Our main theorem is:

THEOREM 1.1. Let R be a locally excellent ℚ-Gorenstein integral domain of characteristic p>0. Then R is F-regular if and only if it is a splinter.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 2 , September 1999 , pp. 201 - 205
Copyright
The Cambridge Philosophical Society 1999

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