Free subalgebras of quotient rings of Ore extensions

Details Free subalgebras of quotient rings of Ore extensions Free subalgebras of quotient rings of Ore extensions

2011-01-30

arxiv.org/abs/1101.5829v2

Mathematics

Rings and Algebras

12 pages; minor changes to statement of main theorem; changes to proofs

Scientific paper

Let $K$ be a field, let $\sigma$ be an automorphism of $K$, and let $\delta$ be a derivation of $K$. We show that if $D$ is one of $K(x;\sigma)$ or $K(x;\delta)$, then $D$ either contains a free algebra over its center on two generators, or every finitely generated subalgebra of $D$ satisfies a polynomial identity. As a corollary, we are able to show that the quotient division ring of any iterated Ore extension of an affine domain satisfying a polynomial identity either again satisfies a polynomial identity or it contains a free algebra over its center on two variables.

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