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Paper   IPM / M / 7260
School of Mathematics
  Title:   Generalized Cohen-Macaulay dimension
1.  J. Asadollahi
2.  Sh. Salarian
  Status:   Published
  Journal: J. Algebra
  Vol.:  273
  Year:  2004
  Pages:   384-394
  Supported by:  IPM
A new homological dimension, called GCM-dimension, will be defined for any finitely generated module M over a local Noetherian ring R. GCM-dimension (short for Generalized Cohen-Macaulay dimension) characterizes Generalized Cohen-Macaulay rings in the sense that: a ring R is Generalized Cohen-Macaulay if and only if every finitely generated R-module has finite GCM-dimension. This dimension is finer than CM-dimension and we have equality if CM-dimension is finite. Our results will show that this dimension has expected basic properties parallel to those of the homological dimensions. In particular, it satisfies an analog of the Auslander-Buchsbaum formula. Similar methods will be used for introducing quasi-Buchsbaum and Almost Cohen-Macaulay dimensions, which reflect corresponding properties of their underlying rings.

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