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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:
16E10 Homological dimension in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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