关于w-linked扩环

Let R ■ T be an extension of commutative rings.T is called w-linked over R if T as an R-module is a w-module.In the case of R ■ T ■ Q 0 （R）,T is called a w-linked overring of R.As a generalization of Wang-McCsland-Park-Chang Theorem,we show that if R is a reduced ring,then R is a w-Noetherian ring with w-dim（R） 1 if and only if each w-linked overring T of R is a w-Noetherian ring with w-dim（T ） 1.In particular,R is a w-Noetherian ring with w-dim（R） = 0 if and only if R is an Artinian ring.     

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

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 Lucas, T. G. (1993). Strong Prüfer rings and the ring of finite fractions. J. Pure Appl. Algebra 84:59–71.[Crossref], [Web of Science ®] , [Google Scholar]] 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).)