b-generalized skew derivations acting as 2-Jordan multiplier on multilinear polynomials in prime rings

2022/12/06 by Pandey, Mani Shankar, Pandey, Ashutosh
#16N60 #16W25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2212.02892

Abstract

Let R be a prime ring of characteristic not equal to 2, U be its Utumi quotient ring and C be the extended centroid of R. Let ϕbe a multilinear polynomial over C, which is not central valued on R and F, G be two b-generalized skew derivations on R. The purpose of this article is to describe all possible forms of the b-generalized skew derivations F and G satisfying the identity F (u)u + uG(u) = G(u ²), for all u ∈ ϕ(ζ) | ζ = (ζ1 . . . , ζn) \inRⁿ. Consequently, we discuss the cases when this identity acts as Jordan derivation and 2- Jordan multiplier on prime rings

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