Article Search
eISSN 0454-8124
pISSN 1225-6951

### Article

Kyungpook Mathematical Journal 2022; 62(1): 43-55

Published online March 31, 2022

### On n-skew Lie Products on Prime Rings with Involution

Shakir Ali and Muzibur Rahman Mozumder*

epartment of Mathematics, Aligarh Muslim University, Aligarh-202002, U. P., India
e-mail : shakir.ali.mm@amu.ac.in and muzibamu81@gmail.com

Received: July 7, 2021; Revised: October 5, 2021; Accepted: October 7, 2021

### Abstract

Let R be a *-ring and n≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that $*[x,d(x)]n∈Z(R)$ for all x∈ R (for n=1, 2), where $d:R→R$ is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.

Keywords: Prime ring, derivation, involution, centralizing mappings, 2-skew Lie product, 2-skew centralizing mappings, n-skew commuting mappings, n-skew centralizing mapping