THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES

نویسندگان
Aghapournahr, M. ID 1
Ahmadi-amoli, Kh. ID 2
Sadeghi, M. ID 3

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.

3 Department of Mathematics, Payame Noor University, Tehran, 19395-3697, Iran.

doi
10.22044/jas.2015.482
چکیده

‎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.

کلیدواژه‌ها
local cohomology modules defined by a pair of ideals, system of ideals, depth of a pair of ideals, $(I, J)$-Cohen--Macaulay modules