An Algorithmic Proof of Suslin's Stability Theorem over Polynomial Rings

Details An Algorithmic Proof of Suslin's Stability Theorem over Polynomial Rings An Algorithmic Proof of Suslin's Stability Theorem over Polynomial Rings

1994-05-10

arxiv.org/abs/alg-geom/9405003v1

Mathematics

Algebraic Geometry

23 pages, LaTex

Scientific paper

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 the multivariate polynomial ring $SL_n(k[x_1,\ldots ,x_m])$ with $n\geq 3$. As Gaussian elimination gives us an algorithmic way of finding an explicit factorization of the given matrix into elementary matrices over a field, we develop a similar algorithm over polynomial rings.

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