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- W4210311395 abstract "Let R be a prime ring with the extended centroid C. An (anti)automorphism g of R is said to be Frobenius if, in the case of char(R) = ∞, = αg = α for all α ∈ C, or in the case of char(R) = p ≥ 0, αg = αpn for all α ∈ C, where n is a fixed integer, which may be zero, positive, or negative. (Anti)automorphisms g1, g2, ... are said to be strongly independent if for any i ≠ j, gig−1j is not Frobenius. The following is proved: MAIN THEOREM. Let ψ(zijk) be a polynomial with Frobenius (anti)automorphisms. Assume that ψ(xΔjgki) = 0 holds on a nonzero two-sided ideal of R, where xi are distinct indeterminates, Δj are distinct regular derivation words (with respect to a linearly ordered basis of outer derivations), and gk are strongly independent (anti)automorphisms of R. Then ψ(zijk) = 0 holds on the two-sided Utumi quotient ring of R. If ψ(zijk) does not involve antiautomorphisms, then ψ(zijk) = 0 also holds on the left Utumi quotient ring of R." @default.
- W4210311395 created "2022-02-08" @default.
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- W4210311395 date "1993-09-01" @default.
- W4210311395 modified "2023-10-17" @default.
- W4210311395 title "Differential Identities with Automorphisms and Antiautomorphisms, II." @default.
- W4210311395 doi "https://doi.org/10.1006/jabr.1993.1181" @default.
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