Cofiniteness with respect to Extension of Serre Subcategories at Small Dimensions

Abstract

Let A denote a commutative Noetherian ring, a be an ideal of A , X be an arbitrary dense subcategory of A -modules, and N be the full subcategory of finite A -modules. In this paper, we study N ⋆ X - c -cofinite modules with respect to the extension subcategory N ⋆ X when dim A / c ≤ 2 . We also study c -cofiniteness with respect to a new dimension.