Cohen-Macaulay homological dimensions

• Parviz Sahandi ^[1] ; Tirdad Sharif ^[2] ; Siamak Yassemi ^[3]
  1. [1] University Of Tabriz (Irán)
  2. [2] Institute for Research in Fundamental Sciences (IPM) (Irán)
  3. [3] University of Tehran (Irán)

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• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 2, 2020, págs. 189-208
• Idioma: inglés
• DOI: 10.7146/math.scand.a-119382
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• Resumen

  • 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 characterize 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.