Finiteness of relative Gorenstein homological dimensions

Authors：Fan, Hongyan; Tang, Xi^*

Source：JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 2550034.

DOI：10.1142/S0219498825500343

• Abelian category
• relative Gorenstein objects
• relative global Gorenstein dimensions

Let A be an abelian category and (X, Y) a pair of classes of objects in A. Inspired by Bouchiba's work on generalized Gorenstein projective modules, we give a new way of measuring (X, Y)-Gorenstein projective dimension by defining a complete n-(X, Y) resolution. Then we relate the relative global Gorenstein homological dimension to the invariants silp(A) and spli(A) under some conditions. Furthermore, we prove that, in the setting of a left and right coherent ring R, the supremum of Ding projective dimensions of all finitely presented (left or right) R-modules and the (left or right) Gorenstein weak global dimension are identical, generalizing a theorem of Ding, Li and Mao.

• Institution
  桂林理工大学; 桂林航天工业学院