Remarks on normal distributive nearlattices

Quasicomplemented distributive nearlattices

“…We recall the basics results about distributive nearlattices, where our main references are [8,2,3,5,6].…”

“…We consider some particular classes of filters and ideals studied in [5,6], and also recall the concept of congruence in distributive nearlattices. Definition 4 Let A be a distributive nearlattice.…”

“…and ρ is a onto homomorphism between the distributive nearlattices A and R(A) such that Θ ⊤ = Ker(ρ) ( [5,6]). The next result give a necessary and sufficient conditions through α-filters so that ρ is 1-1.…”

“…In particular, in [3], the authors presented an alternative definition of relative annihilator in distributive nearlattices different from that given in [9] and established new equivalences of the distributivity. Later, using the results developed in [3], the notion of annihilator was studied in [4][5][6].…”

On the logic of distributive nearlattices

“…Distributive nearlattices were studied by several authors from different points of view; cf. [3–6, 8, 9, 17, 18, 21, 22, 24, 27].…”