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Global Gorenstein dimensions. (English) Zbl 1205.16007
The authors prove that the global Gorenstein projective dimension of a ring $$R$$ is equal to the global Gorenstein injective dimension of $$R$$ and that the global Gorenstein flat dimension of $$R$$ is smaller than the common value of the terms of this equality. The main result of this paper is an analog of a classical equality that is used to define the global dimension of a ring.

##### MSC:
 1.6e+11 Homological dimension in associative algebras 1.6e+31 Homological functors on modules (Tor, Ext, etc.) in associative algebras 1.6e+66 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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