Cofiniteness of torsion functors of a pair of cofinite modules (II)

Abstract

Let I be an ideal of a commutative Noetherian ring R such that the R-modules are I-cofinite, for all finitely generated R-modules U and all . Also, assume that the category of all I-cofinite modules is an Abelian subcategory of the category of R-modules and R-homomorphisms. It is shown that for each pair of I-cofinite modules M and N the R-modules are I-cofinite for all . Also, some applications of this result will be included.