Lattices Derived from Hyperlattices

Abstract

In this article, by considering the notion of a hyperlattice and a superlattice, we give some examples of them, and we study their structures and their quotient structure with a regular relation. We introduce the relation ν on a hyperlattice L, and we let ν* be the transitive closure of ν. We show that ν* is a fundamental relation on a hyperlattice. The quotient L/ν* is called the fundamental lattice. Notice that the most important relations in hyperstructure theory are the fundamental ones. Finally, we give some interesting results about the fundamental lattices.

Key Words:

• Fundamental relation
• Hyperlattice
• Lattice
• Superlattice
• Strong regular relation

2000 Mathematics Subject Classification:

• 06D35
• 20N20

Notes

Communicated by J. Zhang.