Filter Regular Sequence and Generalized Local Cohomology with Respect to a Pair of Ideals

Abstract

Let (R, m) be a Noetherian local ring. Two notions of filter regular sequence and generalized local cohomology module with respect to a pair of ideals are introduced, and their properties are studied. Some vanishing and non-vanishing theorems are given for this generalized version of generalized local cohomology module