Almost Prüfer v-multiplication domains and the ring $D+X{D}_S\left[X\right]$

Qing Li. "Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$." Colloquium Mathematicae 121.2 (2010): 239-247. <http://eudml.org/doc/284216>.

@article{QingLi2010,
abstract = {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.},
author = {Qing Li},
journal = {Colloquium Mathematicae},
keywords = {almost GCD-domain; almost Prüfer domain; well behaved domain},
language = {eng},
number = {2},
pages = {239-247},
title = {Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$},
url = {http://eudml.org/doc/284216},
volume = {121},
year = {2010},
}

TY - JOUR
AU - Qing Li
TI - Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$
JO - Colloquium Mathematicae
PY - 2010
VL - 121
IS - 2
SP - 239
EP - 247
AB - 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.
LA - eng
KW - almost GCD-domain; almost Prüfer domain; well behaved domain
UR - http://eudml.org/doc/284216
ER -