A New Approach on Congruence of a Lattice with a Separator

Abstract

In this paper we study the congruence of a lattice with a separator. An element ‘s’ in a lattice L is called a separator if ‘s’ is covered by the least and greatest element. For every lattice L, adding a separator ‘s’ to L form a lattice. In this we observe that for every nontrivial chain, congruence of congruence of a chain with separator is isomorphic to congruence of a chain. Also we study the congruence of a lattice with more than one separator.

Keywords- congruce, separator, separting lattice and congruence preserving extension mathematics