Characterizations of Prime and Minimal Prime Ideals of Hyperlattices

Abstract

In this paper, we define an ideal and prime ideal of hyperlattices (hyper join and hyper meet operation) .We obtain results on ideals of lattice in the sense of hyperlattice .We prove some results on prime ideals of hyperlattices. A result analogous to separation theorem is obtained for hyperlattices in respect of prime ideals. Further, we extend the classical result of Nachbin for hyperlattices. Also we furnish some characterizations of minimal prime ideals of hyperlattices.