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COPURE PROJECTIVE MODULES OVER FGV-DOMAINS AND GORENSTEIN PRÜFER DOMAINS

  • Shiqi Xing (College of Applied Mathematics Chengdu University of Information Technology)
  • Received : 2022.06.21
  • Accepted : 2022.10.28
  • Published : 2023.07.31
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Abstract

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-Prüfer domains by G-flat modules, and we prove that a domain is G-Prüfer if and only if every submodule of a projective module is G-flat. Also, we study the D + M construction of G-Prüfer domains. It is seen that there exists a non-integrally closed G-Prüfer domain that is neither Noetherian nor divisorial.

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Acknowledgement

The author would like to thank the referee for comments and corrections, which have improved this article. This work is supported by the Scientific Research Foundation of Chengdu University of Information Technology (No. KYTZ202015, 2022ZX001).

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