Some splitting theorems for local cohomology modules with respect to a pair of ideals

Abstract

Suppose that [Formula: see text] is a commutative ring with identity, [Formula: see text], [Formula: see text] are ideals of [Formula: see text], and let [Formula: see text] be a finitely generated [Formula: see text]-module. Let [Formula: see text] be the [Formula: see text]th local cohomology functor with respect to [Formula: see text]. In this paper, for fixed integers [Formula: see text] and [Formula: see text], we study the existence of the following isomorphisms of local cohomology modules: (i) [Formula: see text]; (ii) [Formula: see text]; and, (iii) [Formula: see text] for some filter regular element [Formula: see text] on [Formula: see text]. Moreover, we provide some applications of the above isomorphisms.