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.
2011
pure-semisimple ring; tilting module; Auslander-Reiten quiver
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/345523
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