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 On the principal ideal theorem Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 655-660 Gyu Whan Chang Pohang University of Science and Technology Abstract : Let $R$ be an integral domain with identity. In this paper we will show that if $R$ is integrally closed or if $t$-dim$R \leq 1$, then $R[\{X_{\alpha}\}]$ satisfies the principal ideal theorem for each family $\{X_{\alpha}\}$ of algebraically independent indeterminates if and only if $R$ is an $S$-domain and it satisfies the principal ideal theorem. Keywords : the principal ideal theorem (PIT), $t$-dimension, $S$-domain, an integrally closed domain MSC numbers : 13A15 Full-Text :