Chen-Lian Chuang
Abstract
Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. Our aim (Theorem 1) is to determine any automorphism S of R[t;σ,δ] satisfying S(A)⊆R for a one-sided ideal A≠0 of R by dropping the assumption t∈R[t;σ,δ]. As an application, if R is a domain, it is shown that any X-inner automorphism of R[t;σ,δ] stabilizes R.
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Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. Our aim (Theorem 1) is to determine any automorphism S of R[t;σ,δ] satisfying S(A)⊆R for a one-sided ideal A≠0 of R by dropping the assumption t∈R[t;σ,δ]. As an application, if R is a domain, it is shown that any X-inner automorphism of R[t;σ,δ] stabilizes R.
Key concepts: Automorphism, Mathematics, Ideal (ethics), Prime ring, Skew, Prime (order theory), Pure mathematics, Domain (mathematical analysis)