Invariants of algebraic automorphisms. (Q385542)

Let \(R\) be a prime ring with extended centroid \(C\) and let \(\sigma\) be a \(C\)-algebraic automorphism. The author of the paper proves the nilpotence of the prime radical of \(R^{(\sigma)}=\{x\in R:\sigma(x)=x\}\) with a bound and characterizes the semiprimeness and primeness of \(R^{(\sigma)}\). The author also shows that if \(R^{(\sigma)}\) is prime, then \(\text{PI-deg}(R)=\text{PI-deg}(R^{(\sigma)})\times\text{Inn-deg}(\sigma)\).