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

@inproceedings{Park1994AnAP,
  title={An Algorithmic Proof of Suslin's Stability Theorem over Polynomial Rings},
  author={Harold S. Park and Cynthia J. Woodburn},
  year={1994}
}
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… CONTINUE READING

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Algorithmic Algebra

B. Mishra
  • Springer
  • 1993
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