Abstract
Let R be a prime ring with extended centroid C and let σ be a C-algebraic automorphism of R. We let \(R^{(\sigma)}\mathop{=}\limits^{\rm def.}\{x\in R\mid \sigma(x)=x\}\), 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).
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Liu, KS. Invariants of Algebraic Automorphisms. Algebr Represent Theor 16, 1233–1242 (2013). https://doi.org/10.1007/s10468-012-9354-2
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DOI: https://doi.org/10.1007/s10468-012-9354-2