Symmetry and duality on n-Gorenstein rings

We will study homological properties of noetherian rings. As a bridge between the n-Gorenstein property and the dominant dimension, we will introduce the dominant numbers of rings and prove their left-right symmetry (Section 1.1). The (1, n)-condition (Section 2.2) on selfinjective resolutions provides a useful tool on our study. Moreover, we will give two dualities on n-Gorenstein rings (Sections 1.2, 1.3), where one of them is closely related to the Auslander-Reiten theory (Section 1.3.1). (C) 2003 Elsevier Inc. All rights reserved.