Skip to main content
eScholarship
Open Access Publications from the University of California

Free subalgebras of division algebras over uncountable fields

  • Author(s): Bell, JP
  • Rogalski, D
  • et al.

Published Web Location

http://arxiv.org/abs/1112.0041
No data is associated with this publication.
Abstract

We study the existence of free subalgebras in division algebras, and prove the following general result: if A is a noetherian domain which is countably generated over an uncountable algebraically closed field k of characteristic 0, then either the quotient division algebra of A contains a free algebra on two generators, or it is left algebraic over every maximal subfield. As an application, we prove that if k is an uncountable algebraically closed field and A is a finitely generated k-algebra that is a domain of GK-dimension strictly less than 3, then either A satisfies a polynomial identity, or the quotient division algebra of A contains a free k-algebra on two generators. © 2014 Springer-Verlag Berlin Heidelberg.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Item not freely available? Link broken?
Report a problem accessing this item