Bull. Korean Math. Soc. 2018; 55(2): 649-657
Online first article September 8, 2017 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b170203
Copyright © The Korean Mathematical Society.
Fang Gui Wang, De Chuan Zhou
Sichuan Normal University, Southwest University of Science and Technology
Let $R$ be a commutative ring. In this paper, the $w$-projective Basis Lemma for $w$-projective modules is given. Then it is shown that for a domain, nonzero $w$-projective ideals and nonzero $w$-invertible ideals coincide. As an application, it is proved that $R$ is a Krull domain if and only if every submodule of finitely generated projective modules is $w$-projective.
Keywords: $w$-projective module, $w$-invertible, Krull domain, $w$-module
MSC numbers: 13A15, 13C10, 13D99
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