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arXiv · 0903.1626

Makar-Limanov's conjecture on free subalgebras

Agata Smoktunowicz
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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

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Agata Smoktunowicz. 2009-03-09. Makar-Limanov's conjecture on free subalgebras. https://arxiv.org/abs/0903.1626

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