Gorenstein Dimensions over Cohen-Macaulay Rings
by
Overtoun M.G. Jenda
Auburn University

Let R be a Cohen-Macaulay local ring of Krull dimension d admitting a dualizing module D and let G₀(R) denote the Foxby class consisting of R-modules M such that Tor_i (D, M) = Extⁱ (D, D \otimesM) = 0 for all i >= 1 and such that the natural map M --> Hom (D, D \otimesM) is an isomorphism. Dually let Im₀(R) denote the dual Foxby class consisting of R-modules N such that Extⁱ (D, N) = Tor_i (D, Hom (D, N)) = 0 for all i >= 1 and such that the natural map D \otimesHom (D, N) --> N is an isomorphism. The main aim of this paper is to show that the global Gorenstein flat dimension of G₀(R), the global Gorenstein projective dimension of the full subcategory of finitely generated R-modules in G₀(R), and the global Gorenstein injective dimension of Im₀(R) coincide and are equal to d.

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Date received: January 4, 1999