THE CONCEPT OF (I; J)-COHEN{MACAULAYMODULES

A generalization of the notion of depth of an ideal on amodule is introduced by applying the concept of local cohomologymodules with respect to a pair of ideals . The concept of (I; J)-Cohen{Macaulay modules is also introduced as a generalization ofthe concept of Cohen{Macaulay modules . This kind of modulesis di erent from the Cohen{Macaulay modules, as shown in anexample. Also an Artinian result is given for such modules.

Keywords:

Local cohomology modules de ned by a pair of ideals , System of ideals , Depth of a pair of ideals , (I , J)-Cohen{Macaulay modules , Cohen{Macaulay modules