Makar-Limanov's conjecture on free subalgebras

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

Original languageEnglish
Pages (from-to)2107-2116
Number of pages10
JournalAdvances in Mathematics
Volume222
Issue number6
DOIs
Publication statusPublished - 20 Dec 2009

Keywords

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

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