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• # Artykuł - szczegóły

## Colloquium Mathematicum

2010 | 121 | 2 | 239-247

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

EN

### Abstrakty

EN
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.

239-247

wydano
2010

### Twórcy

autor
• College of Computer Science and Technology, Southwest University for Nationalities, Chengdu 610041, P.R. China