A note on annihilators in distributive nearlattices

Abstract

In this note we propose a definition of relative annihilator in distributive nearlattices with greatest element different from that given in [6] and we present some new characterizations of the distributivity. Later, we study the class of normal and p-linear nearlattices, the lattice of filters and semi-homomorphisms that preserve annihilators.

Note on $\alpha$-filters in distributive nearlattices

“…In [3] it was shown that if A is a distributive nearlattice, then the set of all filters Fi(A) = Fi(A), ⊻, ⊼, →, {1}, A is a Heyting algebra, where the least element is {1}, the greatest element is A, G ⊻ H…”

“…The following definition given in [3] is an alternative definition of relative annihilator in distributive nearlattices different from that given in [10].…”

Annihilator-preserving congruence relations in distributive nearlattices

“…In [3] the authors obtain new equivalences of distributivity of a nearlattice. In this section we present some new characterizations of distributivity using ideals, filters and the theory of relative annihilators.…”

“…The following definition given in [3] is an alternative definition of relative annihilators in distributive nearlattices different from that given in [10]. Let a ∈ A and F ∈ Fi(A).…”

“…An important class of nearlattices are the distributive nearlattices. Recently in [7] and [3], the authors develop a full duality for distributive nearlattices and propose a definition of relative annihilator different from that given in [10].…”