Abstract
Let A be a commutative ring and M an Artinian .A-module. Let be a torsion radical functor and (T, F) it's corresponding partition of Spec(A) In [1] the concept of Cohen-Macauly modules was generalized . In this paper we shall define -co-Cohen-Macaulay (abbr. -co-CM). Indeed this is one of the aims of this paper, we obtain some satisfactory properties of such modules. An-other aim of this paper is to generalize the concept of cograde by using the left derived functor (-) of the -adic completion functor, where a is contained in Jacobson radical of A.A.
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