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FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS

  • Hu, Kui (College of Science Southwest University of Science and Technology) ;
  • Lim, Jung Wook (Department of Mathematics Kyungpook National University) ;
  • Xing, Shiqi (College of Applied Mathematics Chengdu University of Information Technology)
  • Received : 2019.05.28
  • Accepted : 2019.09.05
  • Published : 2020.05.31

Abstract

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂R M∗ → HomR(HomR(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and ExtiR(M, M) = 0 (i ⩾ 1), then M is projective.

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