Affiliation:
1. Department of Mathematics, The University of Akron, Akron, OH 44325, USA
2. Department of Mathematics, Georgia College, Milledgeville, GA 31061, USA
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
2 articles.
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1. A note on maximal non-Manis extensions;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2022-01-06
2. Pullback diagrams and Kronecker function rings;Rocky Mountain Journal of Mathematics;2019-11-01