Leibniz rings: some basic and structural results

TL;DR

This paper explores the fundamental properties of Leibniz rings, highlighting structural differences from Lie rings, especially in cases where the additive group is small, thereby advancing understanding of Leibniz algebraic structures.

Contribution

It provides new structural insights into Leibniz rings, emphasizing their differences from Lie rings, particularly for rings with small additive groups.

Findings

Leibniz rings exhibit distinct structural properties from Lie rings.

Significant differences are observed in Leibniz rings with small additive groups.

The results deepen understanding of Leibniz ring structures.

Abstract

In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes of Leibniz rings and Lie rings.