Free algebras and free groups in Ore extensions and free group algebras in division rings

Jason P. Bell, Jairo Z. Goncalves

Let $K$ be a field of characteristic zero, let $\sigma$ be an automorphism of $K$ and let $\delta$ be a $\sigma$-derivation of $K$. We show that the division ring $D=K(x;\sigma ,\delta )$ either has the prop…