Factorization and divisibility in generalized Rees rings

Hwankoo Kim; Tae In Kwon; Young Soo Park

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2004; 41(3): 473-482

Printed September 1, 2004

Factorization and divisibility in generalized Rees rings

Hwankoo Kim, Tae In Kwon, and Young Soo Park

Hoseo University, Changwon National University, Kyungpook National University

Abstract

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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