Weakly Krull and Related Pullback Domains

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2004, v.11 no.2, pp.117-125

Chang, Gyu-Whan (Dept. of Mathematics, University of Inchon)

Chang, Gyu-Whan. (2004). WEAKLY KRULL AND RELATED PULLBACK DOMAINS. 한국수학교육학회지시리즈B:순수및응용수학, 11(2), 117-125.

복사

Abstract

Let T be an integral domain, M a nonzero maximal ideal of T, K = T/M, <TEX>$\psi$</TEX>: T \longrightarrow K the canonical map, D a proper subring of K, and R = <TEX>$\psi^{-1}$</TEX>(D) the pullback domain. Assume that for each <TEX>$x \; \in T$</TEX>, there is a <TEX>$u \; \in T$</TEX> such that u is a unit in T and <TEX>$ux \; \in R$</TEX>, . In this paper, we show that R is a weakly Krull domain (resp., GWFD, AWFD, WFD) if and only if htM = 1, D is a field, and T is a weakly Krull domain (resp., GWFD, AWFD, WFD).

keywords: weakly Krull domain, GWFD, AWFD, WFD, pullback domain

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Vol.11 No.2

WEAKLY KRULL AND RELATED PULLBACK DOMAINS

Weakly Krull and Related Pullback Domains

Abstract

한국수학교육학회지시리즈B:순수및응용수학