w-Linked Q₀-Overrings and Q₀-Prüfer v-Multiplication Rings

Abstract

Let R be a commutative ring, Q₀(R) be the ring of finite fractions over R, and w be the so-called w-operation on R. In this article, we introduce a new type of Prüfer v-multiplication ring, called a quasi-Q₀-PvMR and defined as a ring R for which every w-linked Q₀-overring of R is integrally closed in Q₀(R). Our primary motivation for investigating quasi-Q₀-PvMRs is to provide w-theoretic analogues to some work of Lucas [16] concerning Q₀-Prüfer rings. (A ring R is called a Q₀-Prüfer ring if every Q₀-overring of R is integrally closed in Q₀(R).)

Key Words:

• (quasi-)Q₀-Prüfer v-multiplication rings
• Ring of finite fractions
• w-flat Q₀-overrings
• w-linked Q₀-overrings

2010 Mathematics Subject Classification:

• 13A15
• 13F05