Leibniz algebras as non-associative algebras

TL;DR

This paper introduces the foundational concepts of Leibniz algebras, a class of non-associative algebras, and proves several main results, some of which are new contributions to the field.

Contribution

It defines basic Leibniz algebra concepts and provides new variations of known proofs along with some original results.

Findings

Established foundational concepts for Leibniz algebras

Proved several main results with some novel contributions

Presented variations of existing proofs

Abstract

In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs and several results seem to be new.