Alternative algebras admitting derivations with invertible values and invertible derivations

TL;DR

This paper characterizes alternative algebras that admit derivations with invertible values and establishes an analogue of Moens's Theorem for such structures.

Contribution

It provides a complete description of alternative algebras with invertible derivations and extends Moens's Theorem to this context.

Findings

All alternative algebras with invertible derivations are described.

An analogue of Moens's Theorem is proved for these algebras.

The results generalize previous theorems in algebra theory.

Abstract

We descibed all alternative algebras with invertible derivations (the analogue of Bergen-Herstein-Lanski's Theorem) and proved the analogue of Moens's Theorem.