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Abstract: It is proved that over every countable field K there is a nil algebra R suchthat the algebra obtained from R by extending the field K containsnoncommutative free subalgebras of arbitrarily high rank.It is also shown that over every countable field K there is an algebra Rwithout noncommutative free subalgebras of rank two such that the algebraobtained from R by extending the field K contains a noncommutative freesubalgebra of rank two.This answers a question of Makar-Limanov



Autor: Agata Smoktunowicz

Fuente: https://arxiv.org/







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