Makar-Limanov's conjecture on free subalgebras

Details Makar-Limanov's conjecture on free subalgebras Makar-Limanov's conjecture on free subalgebras

2009-03-09

arxiv.org/abs/0903.1626v1

Mathematics

Rings and Algebras

Scientific paper

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

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