We prove that, even under the multiparameter definition of Artin, Schelter and Tate, the quantum coordinate ring O,(SL,(k)) of the special linear group SL,(k) satisfies most of the standard ring-theoretic properties of the classical coordinate ring B(SL,(k)). The results Fix a field k. Let CJ = Qq(SL,,(k)) be the (multiparameter) quantum coordinate ring of the special linear group SL,(k) and let Al, = oq(M,(k)) be the corresponding quantum coordinate ring of all y1 x IZ matrices, as defined in [2]. (The definition of these and other concepts used in this introduction are given in the next section.) By definition, Q, = Ju,l(A,l), where A, is a central element in .A, called the 'quantum determinant'. One would like to assert that the standard properties of the classical coordinate ring 6(SL,(k)), for example integrality and finite global homological dimension, also hold for CJJq. This is particularly true since it is easy to show that these properties do hold for JEl, (this follows from the fact that, as is proved in [2, pp. 890-8911, A, is an iterated Ore extension of k in the sense of [4, Section 12.