A classification of generalized skew-derivations on multilinear polynomials in Prime Rings

Year 2025, Early Access, 1 - 14

Basudeb Dhara , Gurninder S. Sandhu , Nripendu Bera

https://doi.org/10.15672/hujms.1472753

Abstract

In this article, we are intended to examine generalized skew-derivations that act as Jordan homoderivations on multilinear polynomials in prime rings. More specifically, we show that if $F$ is generalized skew-derivation of a prime ring $R$ with associated automorphism $\alpha$ such that the relation $F(X^2)=F(X)^2+F(X)X+XF(X)$
holds for all $X\in f(R)$, where $f(x_1,\ldots,x_n)$ is a noncentral valued multilinear polynomial over extended centroid $C$, then either $F=0$ or $F=-id_{R}$ or $F=-id_{R}+\alpha$ (where $id_{R}$ denotes the identity map of $R$).

Keywords

Derivation, generalized derivation, generalized skew derivation, prime ring

Project Number

This work is supported by a grant from Science and Engineering Research Board (SERB), DST, New Delhi, India. Grant No. is EMR/2016/004043 dated 29-Nov-2016

References

• [1] E. Albaş and N. Argaç, Generalized derivations of prime rings, Algebra Colloq. 11, 399-410, 2004.