Quantized rank R matrices
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First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function algebra of rank $r$ matrices obtained by working modulo the ideal generated by all $(r+1)\times (r+1)$ quantum subdeterminants and a certain localization of this algebra is proved to be isomorphic to a more manageable one. In all cases, the quantum parameter is a primitive $m$th roots of unity. The degrees and centers of the algebras are determined when $m$ is a prime and the general structure is obtained for arbitrary $m$.
18 pages with 3 eps figures. Some proofs in Section 5 have been changed and a remark has been removed
18 pages with 3 eps figures. Some proofs in Section 5 have been changed and a remark has been removed