On the nilradical of a Leibniz algebra

TL;DR

This paper corrects a previously published error regarding the relationship between the nilradical of a Leibniz algebra and its quotient by the Leibniz kernel, clarifying the algebraic structure involved.

Contribution

It provides a correction to the literature by establishing the accurate relationship between the nilradical of a Leibniz algebra and its quotient.

Findings

Corrected the erroneous equality involving the nilradical and quotient.

Clarified the structure of the nilradical in Leibniz algebras.

Ensured accurate understanding of Leibniz algebra properties.

Abstract

The purpose of this short note is to correct an error which appears in the literature concerning Leibniz algebras $L$: namely, that $N(L/I)=N(L)/I$ where $N(L)$ is the nilradical of $L$ and $I$ is the Leibniz kernel.