Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that a domain $R$ is an FGV-domain if every finitely generated torsion-free $R$-module is strongly copure projective, and a coherent domain is an FGV-domain if and only if every finitely generated torsion-free $R$-module is strongly copure projective. To do this, we characterize G-Pr\"{u}fer domains by G-flat modules, and we prove that a domain is G-Pr\"{u}fer if and only if every submodule of a projective module is G-flat. Also, we study the $D+M$ construction of G-Pr\"{u}fer domains. It is seen that there exists a non-integrally closed G-Pr\"{u}fer domain that is neither Noetherian nor divisorial.

Keywords: Copure projective modules, G-flat modules, FGV-domains, G-Pr\"{u}fer domains

MSC numbers: 13D05, 13G05, 13F05

Supported by: This work is supported by the Scientific Research Foundation of Chengdu University of Information Technology (No. KYTZ202015, 2022ZX001).