On hyperlattices: congruence relations, ideals and homomorphism

Abstract

We introduce the notion of congruences in hyperlattices. We prove that a quotient of a hyperlattice by a congruence is a “weak-hyperlattice” and not a hyperlattice in general. We explore the connections between congruences, ideals and homomorphism of hyperlattices. In particular, we establish necessary and sufficient conditions for a zero-congruence class to be an ideal of a hyperlattice.