ALMOST PRUFER v-MULTIPLICATION DOMAINS AND THE RING D + X D-S[X]

作者：Li Qing^*

来源：Colloquium Mathematicum, 2010, 121(2): 239-247.

DOI：10.4064/cm121-2-6

• APVMD
• well behaved
• AV-domain
• almost t-splitting set

This paper is a continuation of the investigation of almost Prufer 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 D of D is a PVMD, D subset of(D) over bar is a root extension and D is t-linked under (D) over bar We introduce the notion of an almost t-splitting set D-(S) denotes the ring D + XDS[X], where S is a muliplicatively 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.

• 出版日期2010
• 单位西南民族大学