Quotients premiers deOq(mn(k))

Resume Consider a field k , some nonzero element q of k which is not a root of unity, and some nonnegative integer n . K. R. Goodearl and E. S. Letzter have proved (1991, Prime factor algebras of the coordinate ring of quantum matrices, preprint) that any prime factor algebra of the coordinate ring O q ( m n ( k )) of quantum n × n matrices over k is a domain. In that paper it is proved that the division ring of fractions of such a domain is always isomorphic to the division ring of fractions of the coordinate ring of some quantum space of dimension at most n 2 over some field K which is an extension of k . A similar result is also proved for quantum Weyl algebras.