A note on U-(co)dominant dimension

Abstract

Let R be a Gorenstein artin algebra, and let U be a fixed left R-module and k ⩾ 0. When U is Gorenstein injective, if the U-codominant dimension of any injective left R-module is at most k + 1, then the U-dominant dimension of any projective left R-module is at most k + 1. Dually, when U is Gorenstein projective, if the U-dominant dimension of any projective left R-module is at most k + 1, then the U-codominant dimension of any injective left R-module is at most k + 1.