A note on generalized derivations with multilinear polynomials in prime rings. Issue 4 (2nd April 2020)

• Record Type: Journal Article
• Authors: Tiwari, Shailesh Kumar; Singh, Sanjay Kumar
• Is Part Of: Communications in algebra. Volume 48:Issue 4(2020)
• Page Start: 1770
• Page End: 1788
• Publication Date: 2020-04-02
• Subjects: Derivation -- extended centroid -- generalized derivation -- Prime ring -- Utumi quotient ring; 16W25 -- 16N60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1705473
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R with the extended centroid C and f ( x 1, …, x n ) be a non-central multilinear polynomial over C . Suppose that F and G are two generalized derivations on R such that F 2 ( u ) u − G ( u 2 ) ∈ C for all u = f ( r 1, …, r n ), then we give the complete description of the mappings F and G .