Quasi-Prüfer Extensions of Rings

Gabriel Picavet () and Martine Picavet-L’Hermitte
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Gabriel Picavet: Université Blaise Pascal, Laboratoire de Mathématiques
Martine Picavet-L’Hermitte: Université Blaise Pascal, Laboratoire de Mathématiques

A chapter in Rings, Polynomials, and Modules, 2017, pp 307-336 from Springer

Abstract: Abstract We introduce quasi-Prüfer ring extensions, in order to relativize quasi-Prüfer domains and to take also into account some contexts in recent papers. An extension is quasi-Prüfer if and only if it is an INC pair. The class of these extensions has nice stability properties. We also define almost-Prüfer extensions that are quasi-Prüfer, the converse being not true. Quasi-Prüfer extensions are closely linked to finiteness properties of fibers. Applications are given for FMC extensions, because they are quasi-Prüfer.

Keywords: Flat epimorphism; FIP; FCP Extension; Minimal extension; Integral extension; Morita; Prüfer hull; Support of a module; Fiber; Primary:13B02; Secondary:13B22; 13A18; 13F05; 14A05 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_16

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DOI: 10.1007/978-3-319-65874-2_16

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