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

1994/05/10 by H. Park, Hyungiu Park, Park, H. +3
Computer Science · Mathematics · #Coding theory and cryptography #Commutative Algebra and Its Applications #Polynomial and algebraic computation #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9405003

23 pages, LaTex

arxiv created 1994/05/10 · arxiv updated 2009/11/30

Abstract

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≥ 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[x₁,… ,x_m]) with n≥ 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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