Generalized derivations act as a Jordan homomorphism on multilinear polynomials

Tiwari, Sweta; Prajapati, B.

doi:10.1080/00927872.2018.1539174

Cited by 6 publications

(1 citation statement)

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“…More precisely, they describe the structure of additive mapping satisfying the identity F (f (r))f (r) − f (r)G(f (r)) = 0 for all r ∈ R n , where f is a multilinear polynomial and F , G are two generalized derivations on prime ring R. In 2018, Tiwari [19] studied the commuting generalized derivations on prime ring, which is generalization of the work of Argaç and De Filippis [16]. The generalization of Posner's theorem for generalized derivation on multilinear polynomial in [26] (where further generalization can be found in [1,2,20,21]) is given below.…”

Section: Introductionmentioning

confidence: 99%

b-Generalized Skew Derivations on Multilinear Polynomials

PRAJAPATI¹

2023

KgJMat

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Let R be a prime ring of characteristic different from 2 with the center Z(R) and F , G be b-generalized skew derivations on R. Let U be Utumi quotient ring of R with the extended centroid C and f (x 1 , . . . , x n ) be a multilinear polynomial over C which is not central valued on R. Suppose that P / ∈ Z(R) such thatfor all r = (r 1 , . . . , r n ) ∈ R n , then one of the following holds:(1) there exist λ, µ ∈ C such that F (x) = λx, G(x) = µx for all x ∈ R;(2) there exist a, b ∈ U , λ, µ ∈ C such that F (x) = ax+λx+xa, G(x) = bx+µx+xb for all x ∈ R and f (x 1 , . . . , x n ) 2 is central valued on R.

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