Jordan algebras admitting derivations with invertible values

TL;DR

This paper characterizes all Jordan algebras that admit derivations which only take invertible or zero values, extending previous results from associative rings to Jordan algebra structures.

Contribution

It provides a complete classification of Jordan algebras with derivations having invertible values, generalizing earlier work on associative rings.

Findings

Classification of Jordan algebras with such derivations

Extension of previous associative ring results

New structural insights into Jordan algebras

Abstract

The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstein and Lanski, in which they determined the structure of associative rings that admit derivations with invertible values. Later, the results of this paper were generalized in many cases, for example, for generalized derivations, associative super-algebras, alternative algebras and many others. The present work is dedicated to description of all Jordan algebras admitting derivations with invertible values.