email: stephenson@hope.edu
Abstract: The purpose of this article and the companion article [St2] is to complete the classification of Artin-Schelter regular algebras of global dimension three. For algebras generated by elements of degree one, this has been achieved by M. Artin, W. Schelter, J. Tate and M. Van den Bergh. Therefore, this paper deals with algebras which are not generated in degree one.
In this article, we show that in many cases, the algebras mentioned above have a rather simple structure, and can be understood by traditional ring-theoretic techniques. As in the work of Artin, Schelter, Tate and Van den Bergh, certain exceptional algebras do arise which cannot be studied by traditional methods. These algebras are described in [St2].
This article appeared in Journal of Algebra 183 (1996), 55-73. Reprints are available from the author.