Identities involving generalized derivations act as Jordan homomorphisms

Pallavee Gupta (), S. K. Tiwari () and B. Prajapati ()
Additional contact information
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
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00407-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:55:y:2024:i:2:d:10.1007_s13226-023-00407-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-023-00407-0

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().