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

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