Finitely generated $G$-projective modules over PVMDs
Bull. Korean Math. Soc.
Published online December 4, 2019
Kui Hu, Jung Wook Lim, and Shiqi Xing
Southwest University of Science and Technology, Kyungpook National University, Chengdu University of Information Technology
Abstract : Let $M$ be a finitely generated $G$-projective $R$-modules over a PVMD $R$. We prove that $M$ is projective if and only if the canonical map $\theta: M\bigotimes_R M^* \rightarrow Hom_R(Hom_R(M,M),R)$ is a surjective homomorphism. Particularly, if $G{\mbox-}gldim(R) < \infty$ and $Ext_ R^i(M,M) = 0 (i \geq1)$, then $M$ is projective.
Keywords : Gorenstein projective module, projective modules, PVMD
MSC numbers : 13G05, 13D03
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