### An Algorithmic Proof of Suslin's Stability Theorem for Polynomial Rings, by H. Park and C. Woodburn

Let k be a field. Then Gaussian elimination over k and the Euclidean
division algorithm for the univariate polynomial ring k[x]
allow us to write any matrix in
SL_n(k) or SL_n(k[x]), n\geq 2, as a product of elementary
matrices. Suslin's stability theorem states that the same is true for
SL_n(k[x_1,\ldots ,x_m]) with n\geq 3 and m\geq 1.
In this paper, we present an algorithmic proof of Suslin's stability
theorem, thus providing a method for finding an explicit factorization
of a given polynomial matrix into elementary matrices.
Groebner basis techniques may be used in the implementation of the algorithm.

H. Park <park@math.berkeley.edu>

C. Woodburn <cwoodbur@mail.pittstate.edu>