Kyungpook Mathematical Journal 2022; 62(1): 43-55
Published online March 31, 2022
Copyright © Kyungpook Mathematical Journal.
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 : firstname.lastname@example.org and email@example.com
Received: July 7, 2021; Revised: October 5, 2021; Accepted: October 7, 2021
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 for all x∈ R (for n=1, 2), where 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