Abstract
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized n×r matrices as well as certain quantized factor algebras Mr+1q(n) of Mq(n) are analyzed. For r=1,…,n−1,Mr+1q(n) is the quantized function algebra of rank r matrices obtained by working modulo the ideal generated by all (r+1)×(r+1) quantum subdeterminants and a certain localization of this algebra is proved to be isomorphic to a more manageable one. In almost all cases, the quantum parameter is a primitive mth root of unity. The degrees and centers of the algebras are determined when m is a prime and the general structure is obtained for arbitrary m.
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