PRIME FACTOR ALGEBRAS OF THE COORDINATE RING OF QUANTUM MATRICES

It is proved that every prime factor algebra of the coordinate ring O( q)(M(n)(k)) of quantum n x n matrices over a field k is an integral do main (albeit not necessarily commutative) when q is not a root of unit y. The same conclusion follows for the quantum groups O(q)(SL(n)(k)) a nd O(q)(GL(n)(k)). The proof uses a q-analog of Sigurdsson's theorem b ounding the Goldie ranks of prime factors of differential operator rin gs; this q-analog in tum is based on results from the authors' recent work on q-skew polynomial rings.