Geodesic
${SL}_n(F[x])$ is not boundedly generated by elementary matrices: explicit proof.
The electronic journal of linear algebra, Tome 11 (2004), pp. 162-167.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using methods of higher algebraic K-theory, van der Kallen proved that $S\Ln (F [x])$ does not have bounded word length with respect to elementary matrices if the field F has infinite transcendence degree over its prime subfield. A short explicit proof of this result is exhibited by constructing a sequence of matrices with infinitely growing word length. This construction is also used to show that $S\Ln (Z[x])$ does not have bounded word length with respect to elementary matrices of "bounded degree".
Classification : 20F05, 15A33
Keywords: word length, elementary matrix, polynomial matrix 
@article{ELA_2004__11__a9,
     author = {Erovenko, Igor V.},
     title = {${SL}_n(F[x])$ is not boundedly generated by elementary matrices: explicit proof.},
     journal = {The electronic journal of linear algebra},
     pages = {162--167},
     publisher = {mathdoc},
     volume = {11},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2004__11__a9/}
}
TY  - JOUR
AU  - Erovenko, Igor V.
TI  - ${SL}_n(F[x])$ is not boundedly generated by elementary matrices: explicit proof.
JO  - The electronic journal of linear algebra
PY  - 2004
SP  - 162
EP  - 167
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2004__11__a9/
LA  - en
ID  - ELA_2004__11__a9
ER  - 
%0 Journal Article
%A Erovenko, Igor V.
%T ${SL}_n(F[x])$ is not boundedly generated by elementary matrices: explicit proof.
%J The electronic journal of linear algebra
%D 2004
%P 162-167
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2004__11__a9/
%G en
%F ELA_2004__11__a9
Erovenko, Igor V. ${SL}_n(F[x])$ is not boundedly generated by elementary matrices: explicit proof.. The electronic journal of linear algebra, Tome 11 (2004), pp. 162-167. http://geodesic.mathdoc.fr/item/ELA_2004__11__a9/