Remarks on normal distributive nearlattices

Abstract

In this paper, we present the notions of -ideal and -congruence on a distributive nearlattice. We prove that the -ideals and -congruences of a  normal distributive lattice A are in a one-to-one correspondence with the ideals and congruences of the distributive nearlattice R(A) of the annihilators of A, respectively.

Key words: Nearlattice, annihilator, ideal, congruence.