… Auslander–Reiten theory, cluster tilting, maximal modifying modules in algebraic geometry,
and to homological invariants such as dominant dimension and representation dimension. …

… graded free resolutions of Gorenstein ideals of codimension … Gorenstein ring SI, where S
is the polynomial ring in rs variables xij, 1 ≤ i ≤ r, 1 ≤ j ≤ s, over a field K and I is a Gorenstein …

… Abstract: As a generalization of the Auslander-Reiten transpose, … develop the generalized
Gorenstein dimension with respect to C in … We call the ΣT (M) the transpose of M with respect to …

… We also prove that every Gorenstein perfect algebra of grade $1 $ can be presented, as a
… In addition, we establish a correspondence, roughly speaking, between Gorenstein perfect …

… to a Gorenstein ring, that is, a right- and left-noetherian ring with finite right and left injective
dimension. … Following [6], we define the Auslander-Bridger transpose for a module over a …

… of Gorenstein projective τ-rigid modules, Gorenstein projective … and Gorenstein torsion pairs
and give a Gorenstein analog to … Auslander and Bridger’s modules of G-dimension zero in …

… a 1-Gorenstein … dimensional k-algebras, including the Auslander-Reiten translates A = DTr
and A -’ = Tr D, where D is vector space duality and Tr is the Auslander-Bridger transpose (a …

… concerned with the following theorem of Auslander [2], where depthR… The transpose TrM of
M is the cokernel of f∗ = HomR(f,R), … Note that the transpose and the syzygy of M are uniquely …

… -dimensional local Gorenstein rings would ensure that it holds for every local … Auslander
sequence and Tor-rigidity. We introduce an important tool concerning the Auslander transpose (…

… The Gorenstein rings of finite representation type are exactly the rational double points,
in any … For simplicity we here only state the criterion in a form convenient for the nonGorenstein …