Some Characterizations of Algebras of Finite Representation Type

Abstract:

      Let $A$ be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that $A$ is of finite representation type if and only if there is a natural number $m$ such that ${\rm rad}^{m}({\rm End}(M))=0$, for any indecomposable $A$-modules $M$. This gives a partial answer to one of problems posed by Skowro\'nski.