Rings with sovable quivers

Frank W. Anderson and Barbara K. D’Ambrosia

Vol. 213 (2004), No. 2, 213–230

DOI: 10.2140/pjm.2004.213.213

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 ∈ A of primitive idempotents.

Milestones

Received: 13 June 2001

Revised: 7 April 2003

Published: 1 February 2004