On ω-Linked Overrings

Let R (C) T be an extension of commutative rings. T is called ω-linked over R if T as an R-module is a ω-module. In the case of R (C) T (C) Q0(R), T is called a ω-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 ω-Noetherian ring with ω-dim(R) ≤1 if and only if each ω-linked overring T of R is a ω-Noetherian ring with ω-dim(T) ≤ 1. In particular, R is a ω-Noetherian ring with ω-dim(R) = 0 if and only if R is an Artinian ring.     

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.