Canadian Mathematical Society
Conference Proceedings Volume 24, 1998
pp. 497 - 511

Abstract.
Let  R  be a hereditary artinian PI-ring, i. e. a hereditary artinian ring with radical factor an artin algebra.  We describe the shape of the connected components of the AR-quiver of R , which has as set of points a transversal of the indecomposable finite length R -modules.  In particular we adapt the Theorem of Ringel and Auslander, Bautista, Platzeck, Reiten and Smaloe to this more general situation.

Theorem. Let  R  be a hereditary artinian PI-ring and C  a connected component of  its AR-quiver which does not contain a projective or an injective module.  Then  C  is quasi-serial, i. e. as a valued translation quiver,  C  is isomorphic to  ZAoo , or to a tube.

Mathematical Reviews:  99i:16033
Zentralblatt: 926:16014

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Last modified:  April 17, 2000, by Markus Schmidmeier