Kernel Inclusions of Algebraic Automorphisms

Abstract

Let R be a prime ring with left Martindale quotient ring R _ℱ and symmetric Martindale quotient ring Q. Define, for an automorphism σ of R, R ^(σ) = {x ∈ R∣x ^σ = x}. Let σ and τ be automorphisms of R, and assume that σ is left R _ℱ -algebraic. We show that R ^(σ) ⊆ R ^(τ) if and only if x ^τ = vx ^{σ i} v ⁻¹ for all x ∈ R, where i is an integer and where v is in the centralizer of R ^(σ) in Q.

Key Words:

• Automorphism
• GPI
• Kernel inclusion
• Prime ring

2000 Mathematics Subject Classification:

• 16W20
• 16N60

Notes

Communicated by M. Bresar.