The global dimension of the endomorphism ring of a generator-cogenerator for a hereditary Artin algebra

Abstract

Dlab V, Ringel CM. The global dimension of the endomorphism ring of a generator-cogenerator for a hereditary Artin algebra. Mathematical Reports of the Academy of Science of the Royal Society of Canada. 2008;30(3):89-96.Let Λ be a hereditary Artin algebra andMa Λ-modulethat is both a generator and a cogenerator. We are going to describe the possibilities for the global dimension of End(M) in terms of the cardinalities of the Auslander–Reiten orbits of indecomposable Λ-modules