Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri Hügel (2007) . We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. © 2010 Elsevier Inc.
- Auslander-Reiten Theory
- Cotilting duality
- Pure-semisimple rings
- Pure-Semisimplicity Conjecture
- Tilting equivalence