In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1055,
author = {Waldemar Ho\l ubowski},
title = {An inverse matrix of an upper triangular matrix can be lower triangular},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {22},
year = {2002},
pages = {161-166},
zbl = {1031.15006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1055}
}
Waldemar Hołubowski. An inverse matrix of an upper triangular matrix can be lower triangular. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 161-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1055/
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