Identities involving generalized derivations act as Jordan homomorphisms
Pallavee Gupta (),
S. K. Tiwari () and
B. Prajapati ()
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Pallavee Gupta: Indian Institute of Technology Patna
S. K. Tiwari: Indian Institute of Technology Patna
B. Prajapati: Dr. B. R. Ambedkar University Delhi
Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 731-748
Abstract:
Abstract Let R be a prime ring with char(R) is not equal to 2 and $$\pi (\omega _1,\ldots ,\omega _n)$$ π ( ω 1 , … , ω n ) be a noncentral multilinear polynomial over the extended centroid C of R. If $$F_1$$ F 1 , $$F_2$$ F 2 and $$F_3$$ F 3 are generalized derivations on R such that $$F_1(F_3(\xi ^2))=F_2(\xi )F_3(\xi )$$ F 1 ( F 3 ( ξ 2 ) ) = F 2 ( ξ ) F 3 ( ξ ) for all $$\xi =\pi (\omega _1,\ldots ,\omega _n)$$ ξ = π ( ω 1 , … , ω n ) , $$\omega _1,\ldots ,\omega _n \in R$$ ω 1 , … , ω n ∈ R , then we describe all possible forms of generalized derivations $$F_1$$ F 1 , $$F_2$$ F 2 and $$F_3$$ F 3 .
Keywords: Differential polynomial identity; Prime ring; Multilinear polynomial; Generalized derivation; Utumi quotient ring; 16N60; 16W25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00407-0
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