Document Type : Original Manuscript
Authors
1 Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8- 8349, Iran.
2 Department of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.
Abstract
We introduce a generalization of the notion of depth of an ideal on a module by applying the concept of local cohomology modules with respect to a pair of ideals.
We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modules. These kind of modules are different from Cohen--Macaulay modules, as an example shows. Also an artinian result for such modules is given.
Keywords