Cohen-Macaulay dimension for modules over a commutative ring lias been defined by A. A. Gcrko. That is a homological invariant sharing many properties with projective dimension and Gorcnstcin dimension. The main purpose of this paper is to extend the notion of Cohen-Macaulay dimension for modules over commutative noetherian local rings to that for bounded complexes over non-commutative noetherian rings.
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