### b-Generalized Skew Derivations on Multilinear Polynomials

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**Authors:**B. PRAJAPATI

**DOI:**10.46793/KgJMat2301.021P

**Abstract:**

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 PZ(R) such that

_{1},…,r

_{n}) ∈ R

^{n}, then one of the following holds:

- there exist λ,μ ∈ C such that F(x) = λx, G(x) = μx for all x ∈ R;
- 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.

**Keywords:**

b-Generalized skew derivations, multilinear polynomials, prime rings, the extended centroid, Utumi quotient ring.

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