Domains whose overrings satisfy ACCP

An integral domain D satisfies ACC on principal ideals (ACCP) if there does not exist an infinite strictly ascending chain of principal ideals of D. A ny Noetherian domain, in particular any Dedekind domain, satisfies ACCP. In this note we prove the following theorem: Let D be an integral domain. The n the integral closure of D is a Dedekind domain if and only if every overr ing of D (ring between. D and its quotient field) satisfies ACCP.