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