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Makar-Limanov's conjecture on free subalgebras

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http://www.sciencedirect.com/science/article/pii/S0001870809002242
Original languageEnglish
Pages (from-to)2107-2116
Number of pages10
JournalAdvances in Mathematics
Volume222
Issue number6
DOIs
Publication statusPublished - 20 Dec 2009

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 [Lenny Makar-Limanov, private communication, Beijing, June 2007].

    Research areas

  • Free subalgebras, Extensions of algebras, Nil rings, DIVISION RINGS, FREE SUBGROUPS, FREE SUBSEMIGROUPS, POLYNOMIAL-RINGS, ALGEBRAS, FRACTIONS

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