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TitleAn Algorithmic Proof of Suslin's Stability Theorem for Polynomial Rings
Author(s) Hyungju Park, Cynthia Woodburn
TypeArticle in Journal
AbstractLet 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 S L_n (k) or S L_n (k[x]), n \geq 2, as a product of elementary matrices. Suslin's stability theorem states that the same is true for S L_n (k[x_1, ... ,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. Gröbner basis techniques may be used in the implementation of the algorithm.
Translation No
Refereed No