Dedicated to Daniel Simson on the occasion of his seventieth birthday MSC: 16D50; 16G10; 16G70 a b s t r a c t We give a complete description of the Morita equivalence classes of all connected selfinjective artin algebras for which the Auslander-Reiten quiver admits a family of quasitubes having common composition factors, closed under composition factors, and consisting of modules not lying on infinite short cycles.

We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.

No abstract

No abstract

A ring Λ satisfies the Generalized Auslander-Reiten Condition (GARC) if for each Λ-module M with Ext i (M, M ⊕ Λ) = 0 for all i > n the projective dimension of M is at most n. We prove that this condition is satisfied by all n-symmetric algebras of quasitilted typea broad class of self-injective algebras where every module is ν-periodic.