Denominators for the Poincare series of invariants of small matrices

We determine explicit denominators for the Poincare series of (a) the invar iants of m generic N x N matrices, and (b) the ring generated by m generic N x N matrices and their traces, for N less than or equal to 4. For N less than or equal to 3 we prove (and for N = 4 we conjecture) that the denomina tors we obtain are of minimum degree. We also give explicit rational fracti ons for both series for small values of m and N.