Kronecker function rings of ring extensions

Abstract

The classical Kronecker function ring construction associates to a domain [Formula: see text] a Bézout domain. Let [Formula: see text] be a subring of a ring [Formula: see text], and let ⋆ be a star operation on the extension [Formula: see text]. In their book [Manis Valuations and Prüfer Extensions II, Lectures Notes in Mathematics, Vol. 2103 (Springer, Cham, 2014)], Knebusch and Kaiser develop a more general construction of the Kronecker function ring of [Formula: see text] with respect to ⋆. We characterize in several ways, under relatively mild assumption on [Formula: see text], the Kronecker function ring as defined by Knebusch and Kaiser. In particular, we focus on the case where [Formula: see text] is a flat epimorphic extension or a Prüfer extension.