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Paper   IPM / M / 15658
School of Mathematics
  Title:   Cohen-Macaulay homological dimensions
  Author(s):  Tirdad Sharif (Joint with P. Sahandi and S. Yassemi)
  Status:   Published
  Journal: Math. Scand.
  Vol.:  126
  Year:  2020
  Pages:   189-208
  Supported by:  IPM
We introduce new homological dimensions, namely the Cohen- Macaulay projective, injective and flat dimensions for homologically bounded complexes. Among other things we show that (a) these invariants charac- terize the Cohen-Macaulay property for local rings, (b) Cohen-Macaulay flat dimension fits between the Gorenstein flat dimension and the large restricted flat dimension, and (c) Cohen-Macaulay injective dimension fits between the Gorenstein injective dimension and the Chouinard invariant.

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