# A central idempotent in the endomorphism algebra of a finite lattice

## TL;DR

This paper constructs a specific idempotent in the endomorphism algebra of a finite lattice, linked to its totally ordered sublattices, providing insights into lattice endomorphisms.

## Contribution

It offers a direct construction of a central idempotent associated with totally ordered sublattices in the endomorphism algebra of a finite lattice.

## Key findings

- Explicit construction of the idempotent
- Connection between sublattices and algebraic structure
- Potential applications in lattice theory and algebra

## Abstract

We give a direct construction of a specific idempotent in the endomorphism algebra of a finite lattice $T$. This idempotent is associated with all possible sublattices of $T$ which are total orders.