MINIMAXNESS AND COFINITENESS PROPERTIES OF GENERALIZED LOCAL COHOMOLOGY WITH RESPECT TO A PAIR OF IDEALS

Let I and J be two ideals of a commutative Noetherian ring R and M, N be two non-zero finitely generated R-modules. Let t be a non-negative integer such that H-I(i), (J)(N) is (I, J)-minimax for all i < t. It is shown that the generalized local cohomology module N) is (I, J)-Cofinite minimax for all i < t. Also, we prove that the R-module Ext(R)(j)(R/I, H-I(i), (J)(N)) is finitely generated for all i <= t and j = 0,1.