A note on division rings satisfying generalized rational identities with anti-automorphisms

Let $D$ be a division ring with infinite center $F$; $σ$ be an anti-automorphism of $D$ and $m$ be a positive integer such that $σ^m\neq \mathrm{Id}$. In this paper, we show that if $D$ satisfies a $σ^m$-GRI, then $D$ is centrally finite.