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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 MakarLimanov [Lenny MakarLimanov, private communication, Beijing, June 2007].
Original language  English 

Pages (fromto)  21072116 
Number of pages  10 
Journal  Advances in Mathematics 
Volume  222 
Issue number  6 
DOIs  
Publication status  Published  20 Dec 2009 
Keywords
 Free subalgebras
 Extensions of algebras
 Nil rings
 DIVISION RINGS
 FREE SUBGROUPS
 FREE SUBSEMIGROUPS
 POLYNOMIALRINGS
 ALGEBRAS
 FRACTIONS
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Dive into the research topics of 'MakarLimanov's conjecture on free subalgebras'. Together they form a unique fingerprint.Projects
 1 Finished

Nil algebras, algebraic algebras and algebras with finite GelfandKirillov dimension
1/08/06 → 31/07/11
Project: Research