Reverse Homoderivations on (Semi)-prime Rings

Ali, Shakir
Rafiquee, Naira Noor
Varshney, Vaishali
Dy, Outdom

Journal of the Indonesian Mathematical Society
Vol. 31 No. 2 (2025): JUNE

In this paper, we explore and examine a new class of maps known as reverse homoderivations. A reverse homoderivation refers to an additive map g defined on a ring T that satisfies the condition, g(ϑℓ)=g(ℓ)g(ϑ)+g(ℓ)ϑ+ℓg(ϑ), for all ϑ,ℓ∈T. We present various results that enhance our understanding of reverse homoderivations, including their existence in (semi)-prime rings and the behavior of rings when they satisfy certain functional identities. Some examples are provided to demonstrate the necessity of the constraints, while additional examples are given to clarify the concept of reverse homoderivations.