On The Annihilators of Derived Functors of Local Cohomology Modules and Finiteness Dimension

Abstract

Let R be a commutative Noetherian ring, M be a weakly Laskerian R-module and 𝔞 be an ideal of R. Moreover, suppose that F and T are two covariant R-linear functors such that for each R-module L, F(L) and T(L) are 𝔟-torsion for some ideal 𝔟 of R containing 𝔞. In this article, we study the annihilators of the R-modules and , where for j ≥ 0, ℛ j F(−) (respectively, ℒ j T(−)) is the jth right (respectively, left) derived functor of F (respectively, T).