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Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$

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Li Q.

Colloquium Mathematicum

2010

tom 121

nr 2

239-247

This paper is a continuation of the investigation of almost Prüfer v-multiplication domains (APVMDs) begun by Li [Algebra Colloq., to appear]. We show that an integral domain D is an APVMD if and only if D is a locally APVMD and D is well behaved. We also prove that D is an APVMD if and only if the integral closure D̅ of D is a PVMD, D ⊆ D̅ is a root extension and D is t-linked under D̅. We introduce the notion of an almost t-splitting set. $D^{(S)}$ denotes the ring $D + XD_S[X]$, where S is a multiplicatively closed subset of D. We show that the ring $D^{(S)}$ is an APVMD if and only if $D^{(S)}$ is well behaved, D and $D_S[X]$ are APVMDs, and S is an almost t-splitting set in D.

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1 Colloquium Mathematicum

1 Li Q.

1 2010

Wyniki wyszukiwania

Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$