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Free subalgebras of division algebras over uncountable fields
- Publication Year :
- 2011
-
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.<br />Comment: 20 pages
- Subjects :
- Mathematics - Rings and Algebras
16K40, 16P90, 16S10, 16S85
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1112.0041
- Document Type :
- Working Paper