α-MINIMAX MODULES AND EXTENSION FUNCTORS OF LOCAL COHOMOLOGY

Let R be a commutative Noetherian ring and a an ideal of R. The concepts of a-minimax and a-cominimax modules were introduced by Azami, Naghipour and Vakili in [1] as generalization of minimax and a-cofinite modules, respectively. The finiteness of extension functors of local cohomology modules was viewed by Dibaei and Yassemi in [4]. In this paper, we discuss the a-minimaxness of extension functors of local cohomology modules, in several cases. Let M be an a-minimax R-module, and let t be a non-negative integer such that HQ(M) is a-cominimax for all i < t. In [1, Theorem 4.1] we have shown that for any a-minimax submodule N of H-a(t) (M) and for any finitely generated R-module L with Supp L subset of V(a), the R -module Hom(R) (L, H-a(t) (M)/N) is a-minimax. In this paper, it is shown that Ext(R)(i) (L, H-a(t) (M)/N) is a-minimax for i = 0,1; in addition, if Hom(R) (R/a, H-a(t+1) (M)) is a-minimax, then Ext(R)(i) (L, H-a(t) (M)/N) is a-minimax for i = 0, 1, 2.