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. denotes the ring , where S is a multiplicatively closed subset of D. We show that the ring is an APVMD if and only if is well behaved, D and are APVMDs, and S is an almost t-splitting set in D.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-6,
author = {Qing Li},
title = {Almost Pr\"ufer v-multiplication domains and the ring $D + XD\_S[X]$
},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {239-247},
zbl = {1205.13028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-6}
}
Qing Li. Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$
. Colloquium Mathematicae, Tome 120 (2010) pp. 239-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm121-2-6/