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

• Autorzy: Qing Li
• Języki publikacji: 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.

Kategorie tematyczne

• 13G05: Integral domains
• 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
• 13A15: Ideals; multiplicative ideal theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 2
• Strony: 239-247

Daty

wydano

2010

Twórcy

autor

Qing Li

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

Identyfikatory

DOI

10.4064/cm121-2-6