Makar-Limanov's conjecture on free subalgebras

Agata Smoktunowicz

doi:10.1016/j.aim.2009.07.010

Makar-Limanov's conjecture on free subalgebras

Agata Smoktunowicz

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	2107-2116
Number of pages	10
Journal	Advances in Mathematics
Volume	222
Issue number	6
DOIs	https://doi.org/10.1016/j.aim.2009.07.010
Publication status	Published - 20 Dec 2009

Keywords / Materials (for Non-textual outputs)

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

Access to Document

10.1016/j.aim.2009.07.010

Makar-Limanov's conjecture on free subalgebrasAccepted author manuscript, 625 KB

http://www.sciencedirect.com/science/article/pii/S0001870809002242

Cite this

@article{cd7a7fcbbdbc4155b4e54e0ab61e6bea,

title = "Makar-Limanov's conjecture on free subalgebras",

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].",

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

author = "Agata Smoktunowicz",

year = "2009",

month = dec,

day = "20",

doi = "10.1016/j.aim.2009.07.010",

language = "English",

volume = "222",

pages = "2107--2116",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

number = "6",

}

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 - https://www.scopus.com/pages/publications/70349506752

U2 - 10.1016/j.aim.2009.07.010

DO - 10.1016/j.aim.2009.07.010

M3 - Article

SN - 0001-8708

VL - 222

SP - 2107

EP - 2116

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 6

ER -

Makar-Limanov's conjecture on free subalgebras

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension

Cite this

Makar-Limanov's conjecture on free subalgebras

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Projects

Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension

Cite this