TILTED ORDERS AND ORDERS OF FINITE GLOBAL DIMENSION

The aim of this note is to extend the results of tilted artinian algebras [2, 4, 3, 1] to orders. Some of the proofs carry over almost unchanged from the artinian case to the case of orders: others need considerable alteration—in particular the results on global dimensions. For the convenience of the reader we shall give complete proofs here—some are taken directly from [2].

I would like to thank C.M. Ringel who has patiently explained to me the situation for artinian algebras.