On Glivenko Congruence of a 0-Distributive Nearlattice

In this paper the authors have studied the Glivenko congruence R in a 0-distributive nearlattice S defined by " () R b a ≡ if and only if 0 = ∧ x a is equivalent to 0 = ∧ x b for each S x ∈ ". They have shown that the quotient nearlattice R S is weakly complemented. Moreover, R S is distributive if and only if S is 0-distributive. They also proved that every Sectionally complemented nearlattice S in which every interval [ ] x , 0 is unicomplemented is SemiBoolean if and only if S is 0-distributive. 1. Introduction J.C. Varlet [5] has given the definition of a 0-distributive lattice to generalize the notion of pseudocomplemented lattice. Then many authors including [1] and [3] studied the 0-distributive properties in lattices and meet semilattices. Recently, [6] have studied the 0-distributive nearlattices. A nearlattice is a meet semilattice together with the property that any two elements possessing a common upper bound have a supremum. This property is known as the upper bound property. A nearlattice S is called distributive if for all