Weak Resolution Dimensions of Subcategories

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let Λ be an Artinian algebra, and A, B and X subcategories of Λ-modules, such that each object X in X is given by an exact sequence 0→A→B→X→0 with A∈ObA and B∈ObB. We prove that the weak resolution dimension of X is bounded above by the sum of the corresponding dimensions for A and B plus 1. As applications, we study weak resolution dimensions of Artinian algebras under left idealized extensions and conditions on special ideals.