Unique Factorization in Torsion-Free Modules

Gerhard Angermüller ()

A chapter in Rings, Polynomials, and Modules, 2017, pp 13-31 from Springer

Abstract: Abstract A generalization of unique factorization in integral domains to torsion-free modules (“factorial modules”) has been proposed by A.-M. Nicholas in the 1960s and subsequently refined by D.L. Costa, C.-P. Lu and D.D. Anderson, S. Valdes-Leon. The aim of this note is to prove new results of this theory. In particular, it is shown that locally projective modules, flat Mittag-Leffler modules and torsion-free content modules are factorial modules. Moreover, factorially closed extensions of factorial domains are characterized with help of factorial modules.

Keywords: Content module; Factorial domain; Factorial module; Inert extension; Locally projective module; Mittag-Leffler module; 13C13; 13F15; 13G05 (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_2

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DOI: 10.1007/978-3-319-65874-2_2

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