# Reduction of Quasi-Lattices to Lattices

## TL;DR

This paper explores the conditions under which quasi-lattices can be transformed into lattices, providing a fundamental homomorphism theorem that clarifies their structural relationship.

## Contribution

It introduces a fundamental theorem of homomorphism for quasi-lattices, showing how they can be mapped onto lattices under specific conditions.

## Key findings

- Quasi-lattices become lattices when associativity and modularity conditions are met.
- A homomorphism theorem for quasi-lattices is established.
- Conditions for mapping quasi-lattices onto lattices are identified.

## Abstract

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental theorem of homomorphism proved in this article states that a quasi-lattice can be mapped onto a lattice when some conditions are satisfied.