The existence totally reflexive covers

Document Type : Research Paper


Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.



Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover
$\varphi:C \rightarrow M$ such that $C$ is finitely generated and the projective dimension of $\Ker\varphi$ is finite and $\varphi$ is surjective.


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