Invariants of Algebraic Automorphisms

Let R be a prime ring with extended centroid C and let σ be a C-algebraic automorphism of R. We let $R^{(sigma)}mathop{=}limits^{rm def.}{xin Rmid sigma(x)=x}$ , the subring of invariants of σ in R, and let Out-deg(σ) and Inn-deg(σ) denote the outer and inner degrees of σ, respectively. In the paper we first prove the nilpotence of the prime radical of R ^(σ) with a bound and characterize the semiprimeness and primeness of R ^(σ). Moreover, we show that if R ^(σ) is a prime PI-ring, then PI-deg(R)?=?PI-deg(R ^(σ)) × Inn-deg(σ).