Pairs of Rings Whose All Intermediate Rings Are G–Rings

Abstract

A G–ring is any commutative ring R with a nonzero identity such that the total quotient ring $\mathbf {T}(R)$ is finitely generated as a ring over R. A G–ring pair is an extension of commutative rings $A\hookrightarrow B$, such that any intermediate ring $A\subseteq R\subseteq B$ is a G–ring. In this paper we investigate the transfer of the G–ring property among pairs of rings sharing an ideal. Our main result is a generalization of a theorem of David Dobbs about G–pairs to rings with zero divisors.