… mension is analogous to the classical projective dimension and shares … Auslander’s theorem
on the global dimension of rings and the Gorenstein counterpart of the Auslander’s theorem…

… We call an algebra with finite global dimension equal to its dominant dimension d ≥ 2 a
higher … of T and that an algebra as in the previous theorem has to be Gorenstein by 1.4. …

… which originated in the works of Auslander and Bridger [3], … a duality theorem, Gorenstein
global dimension for smash … the duality theorem for smash products over Hopf algebroids. …

… (its analog when C is semidualizing is [19, Theorem 1]). … 5 we shall study the properties of
the Auslander and Bass classes … By [11, Theorem 2.10], we know there is an exact sequence …

… is Auslander’s wellknown theorem … Auslander’s theorem in the setting of complete Gorenstein
local domains by examining path algebras, which preserve finiteness of global dimension…

… for higher Auslander algebras analogous to Auslander-Tachikawa … , Theorem 1.1], the left
Gorenstein global dimension of Γ is also the supremum of Gorenstein injective dimensions of …

… Γ that are a Gorenstein analog of Auslander algebras which … dimension, global dimension
and injective dimension, … n-minimal Auslander–Gorenstein algebra (see Theorem 4.5). Then Z …

… Gorenstein weak global dimension Gwgldim ( R ) of a ring R equals the supremum of the
Gorenstein flat dimensions of … Gorenstein version of the well-known Auslander’s theorem on the …

… According to a classical result established by Auslander, Buchsbaum and Serre, a … that is,
the Gorenstein global dimensions are invariant along Frobenius extensions; see Theorem 3.4. …

… We call an algebra with finite global dimension equal to its dominant dimension d ≥ 2 a
higher … of T and that an algebra as in the previous theorem has to be Gorenstein by 1.4. …