Triple Representation for Supermodular Semilattices

The basic idea of triple representation of a structure is to associate two simpler structures and a connecting map. Triple representation was first introduced by Chen and Gratzer to Stone Lattices [2], [3]. The concept was generalised to distributive pseudo-complemented lattices and then to distributive pseudo-complemented semilattices by Katrinak [10]. The triple representation for modular Pseudo Complemented semilattice was suceeded by W.H.Cornish [4]. Now the triple representation was obtained for a supermodular semilattice and thereby the supermodular semilattices are characterised.