Download or read book Trace Rings of Generic 2 by 2 Matrices written by Lieven Le Bruyn and published by American Mathematical Soc.. This book was released on 1987 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study the trace ring of [italic]m generic 2 by 2 matrices [capital Greek]Pi[italic subscript]m,2. It is shown that it is a polynomial ring over the generic Clifford algebra for [italic]m-ary quadratic forms of rank [less than or equal to] 3. We prove that it is a Cohen-Macaulay module, i.e. it is a free module of finite rank over a polynomial subring of the center. This explains the existence of a functional equation for its Poincaré series.