Free subalgebras of quotient rings of Ore extensions

Abstract

Let K be a field extension of an uncountable base field k, let σ be a k-automorphism of K , and let δ be a k-derivation of K .We show that if D is one of K (x; σ ) or K (x; δ), then D either contains a free algebra over k on two generators, or every finitely generated subalgebra of D satisfies a polynomial identity.As a corollary, we show that the quotient division ring of any iterated Ore extension of an affine PI domain over k is either again PI, or else it contains a free algebra over its center on two variables.

Locations

• Algebra & Number Theory - View - PDF
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF