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.
Auslander-Reiten-components over pure-semisimple hereditary rings
ANGELERI, LIDIA;
2011-01-01
Abstract
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.
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