On Higher Order Homoderivations In Semi-Prime Rings

Abstract

Considering R as an associative ring, a map h which is additive on R with the property h(zw) = h(z)h(w) + h(z)w + zh(w) valid for every z,w ∈ R is called a homoderivation on R. In this paper our purpose is to demonstrate results about this kind of mappings on rings. The link between n-Jordan homoderivations that are mappings satisfying (equation) for all u ∈ R and homoderivations is investigated aa well as a result associating the mappings that
for n > 1 satisfy (equation) for every u ∈ R called n-Jordan generalized homoderivations with generalized homoderivations i.e maps with the property Γ(uv) = Γ(u)h(v)+Γ(u)v+uh(v) for every u,v ∈ R under suitable conditions is proved.