When do the transpose and dual agree? (Q762255)

Let R be an Artin-algebra, K its center and \({}_ KC\) an injective cogenerator. In the paper those indecomposable algebras R are determined for which \(M^*=Hom(M,R)\), resp. \(D(M)=Hom_ K(M,C)\) coincides with the Auslander-Bridger transpose tr M for all finitely generated R-modules M without projective direct summands. These are the Nakayama-algebras with one simple module in case D(M)\(\cong tr M\) and the self-injective Nakayama-algebras with c(R)\(\equiv 0 (n)\) in case \(M^*\cong tr M\), where c(R) is the (common) composition length of the indecomposable projective R-modules and n the number of simple modules.