Abstract

An artinian ring R is square-free in case none of its indecomposable projective modules has a repeated composition factor. Let Q be the quiver of such a square-free ring R. In this paper we show that if R is indecomposable and transitive on the cyclic components of Q and if Q contains no n-crown, then R≅D ×_KA where D is the natural division ring of R, K = CenD, and A is a square-free K-algebra; that is, dim_K(eAf) ≤ 1 for every pair e,f in A of primitive idempotents.

Authors