TY - JOUR
T1 - Makar-Limanov's conjecture on free subalgebras
AU - Smoktunowicz, Agata
PY - 2009/12/20
Y1 - 2009/12/20
N2 - 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].
AB - 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].
KW - Free subalgebras
KW - Extensions of algebras
KW - Nil rings
KW - DIVISION RINGS
KW - FREE SUBGROUPS
KW - FREE SUBSEMIGROUPS
KW - POLYNOMIAL-RINGS
KW - ALGEBRAS
KW - FRACTIONS
UR - http://www.scopus.com/inward/record.url?scp=70349506752&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2009.07.010
DO - 10.1016/j.aim.2009.07.010
M3 - Article
VL - 222
SP - 2107
EP - 2116
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 6
ER -