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Paper IPM / M / 7260  


Abstract:  
A new homological dimension, called GCMdimension, will be defined
for any finitely generated module M over a local Noetherian ring
R. GCMdimension (short for Generalized CohenMacaulay
dimension) characterizes Generalized CohenMacaulay rings in the
sense that: a ring R is Generalized CohenMacaulay if and only
if every finitely generated Rmodule has finite GCMdimension.
This dimension is finer than CMdimension and we have equality if
CMdimension 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
AuslanderBuchsbaum formula. Similar methods will be used for
introducing quasiBuchsbaum and Almost CohenMacaulay dimensions,
which reflect corresponding properties of their underlying rings.
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