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 $F$-Rationality of a Pure Subring of an $F$-Rational Ring Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 851-854 Myung In Moon Seoul National University Abstract : In this paper we will show that the pure subring $R$ of an $F$-rational ring $S$ is $F$-rational when $R$ is a one-dimensional ring, or $S$ is a Gorenstein ring. And we will give a condition that a pure subring of an $F$-rational ring is to be $F$-rational. Keywords : $F$-rationality, purity, tight closure, parameter ideal MSC numbers : 13A35 Downloads: Full-text PDF