SLn(F [x]) Is Not Boundedly Generated by Elementary Matrices: Explicit Proof
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Igor Erovenko, Associate Professor and Director of Undergraduate Study (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
Abstract: Using methods of higher algebraic K-theory, van der Kallen proved that SLn(F [x]) does not have bounded word length with respect to elementary matrices if the field F has infinite transcendence degree over its prime subfield. We
exhibit a short explicit proof of this result by constructing a sequence of matrices with infinitely growing word length. We also use this construction to show that SLn(Z[x]) does not have bounded word length with respect to elementary matrices of “bounded degree”.
SLn(F [x]) Is Not Boundedly Generated by Elementary Matrices: Explicit Proof
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Created on 1/1/2004
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Additional Information
- Publication
- Electronic Journal of Linear Algebra (2004) 11, 162-167 (electronic)
- Language: English
- Date: 2004