Makar-Limanov's conjecture on free subalgebras
Rings and Algebras
2009-03-10 v1
Abstract
It is proved that over every countable field K there is a nil algebra R such that the algebra obtained from R by extending the field K contains noncommutative free subalgebras of arbitrarily high rank. It is also shown that over every countable field K there is an algebra R without noncommutative free subalgebras of rank two such that the algebra obtained from R by extending the field K contains a noncommutative free subalgebra of rank two. This answers a question of Makar-Limanov
Cite
@article{arxiv.0903.1626,
title = {Makar-Limanov's conjecture on free subalgebras},
author = {Agata Smoktunowicz},
journal= {arXiv preprint arXiv:0903.1626},
year = {2009}
}