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.
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