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.