Overring properties of $G$-domains

Abstract

A commutative domain R is called a strong G-domain if every overring between R and the quotient field K of R is of the form R[\/t] for some nonzero element t of R. After characterizing valuation rings which are strong G-domains, the authors show that R is a strong G-domain if and only if it is a finite intersection of valuation rings each of which is a strong Gdomain. Using some results of R. W. Gilmer, Jr., the authors identify the strong G-domains in the class of all Prfer domains. They reprove via Krull domains the theorem characterizing Noetherian G-domains, a result first proved by Artin and Tte. The authors also raise some relevant questions on related overring properties of G-domains.