# On Higher {g_n, h_n}-derivations

## TL;DR

This paper introduces and characterizes higher {g_n, h_n}-derivations and Jordan higher {g_n, h_n}-derivations, proving that on semiprime algebras, Jordan higher derivations are actual higher derivations.

## Contribution

It defines new classes of higher derivations and provides a characterization linking them to existing {g, h}-derivations, with a key result on semiprime algebras.

## Key findings

- Jordan higher {g_n, h_n}-derivations are actual higher {g_n, h_n}-derivations on semiprime algebras.
- Characterization of higher {g_n, h_n}-derivations via {g, h}-derivations.
- Introduction of higher {g_n, h_n}-derivation concepts.

## Abstract

In this article, we introduce the concepts of higher {g_n, h_n}-derivation and Jordan higher {g_n, h_n}-derivation, and then we give a characterization of higher {g_n, h_n}-derivations in terms of {g, h}-derivations. Using this result, we prove that every Jordan higher {g_n, h_n}-derivation on a semiprime algebra is a higher {g_n, h_n}-derivation.