Document Type
Dissertation
Publication Date
1994
Abstract
In 1977, A.A. Suslin proved that Em (R), the subgroup of the general linear group GLm(R) which is generated by the elementary matrices, is equal to the special linear group SLm (R), whenever R is a polynomial ring in n variables over a field and m is at least three. This dissertation contains an algorithmic proof of this result which is now known as Suslin's Stability Theorem, thus providjng an algorithm for factoring a polynomial matrix with determinant one into a product of elementary matrices. There are three key parts to the algorithm: reduction to a special case by using an algorithmic version of the Quillen-Suslin Theorem (a finitely generated projective module over a polynomial ring over a field is free), construction of factorizations over finitely many local rings, and patching together the local solutions to obtain a global factorization. Implementation of the algorithm involves the use of the method of Grobner bases, an important tool in computational algebra. and computational algebraic geometry.
Recommended Citation
Huffman, Cynthia Ph.D., "An Algorithm for Suslin's Stability Theorem" (1994). Faculty Submissions. 9.
https://digitalcommons.pittstate.edu/math_faculty/9
