An improved term ordering for the ideal of commuting matrices

摘要

Let X and Y be generic n by n matrices of indeterminates x_1,...,x_r, y_1,...,y_r. Let S = k[x_1,...,x_r, y_1,...,y_r] where k is a field and r = n~2. Let I is contained in S be the ideal generated by the entries of the matrix XY — YX. We will show how an old result on a good term order for this ideal can be improved using elementary methods.