# On Leibniz algebras whose centralizers are ideals

## TL;DR

This paper investigates Leibniz algebras where the centralizer of every element forms an ideal, introducing CL-algebras and exploring their nilpotency properties.

## Contribution

It defines CL-algebras as Leibniz algebras with all centralizers as ideals and analyzes their nilpotency characteristics.

## Key findings

- Centralizers being ideals characterizes CL-algebras.
- Nilpotency conditions for CL-algebras are established.
- Provides a framework for understanding Leibniz algebra structure.

## Abstract

This paper concerns the study of Leibniz algebras, a natural generalization of Lie algebras, from the perspective of centralizers of elements. We study conditions on Leibniz algebras under which centralizers of all elements are ideals. We call a Leibniz algebra, a CL-algebra if centralizers of all elements are ideals. We discuss nilpotency of CL-algebras.