English

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

Keywords

Cite

@article{arxiv.0903.1626,
  title  = {Makar-Limanov's conjecture on free subalgebras},
  author = {Agata Smoktunowicz},
  journal= {arXiv preprint arXiv:0903.1626},
  year   = {2009}
}
R2 v1 2026-06-21T12:20:00.102Z