Factorization and divisibility in generalized Rees rings
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 473-482
Published online September 1, 2004
Hwankoo Kim, Tae In Kwon, and Young Soo Park
Hoseo University, Changwon National University, Kyungpook National University
Abstract : Let $D$ be an integral domain, $I$ a proper ideal of $D$, and $R =
D[It, t^{-1}]$ a generalized Rees ring, where $t$ is an
indeterminate. For suitable conditions, we show that $R$ satisfies
the ACCP (resp., is a BFD, an FFD, a (pre-)Schreier domain, a
G-GCD domain, a PVMD, a v-domain) if and only if $D$ satisfies the
ACCP (resp., is a BFD, an FFD, a (pre-)Schreier domain, a G-GCD
domain, a PVMD, a v-domain)
Keywords : ACCP, BFD, FFD, (pre-)Schreier, G-GCD domain, PVMD, v-domain
MSC numbers : 13F05, 13F15, 13G05
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