n-KERNELS OF SKELETAL CONGRUENCES ON A DISTRIBUTIVE NEARLATTICE

In this paper, the author studied skeletal congruences θ^* of a distributive nearlattice S, where * represents pseudocomplement. Then described θ(I)^*, θ(I) is smallest congruence S containing n-ideal I as class and showed that I^+ n-kernel θ(I)^*. established following fundamental results: When n an upper element has shown n-kernels are precisely those n-ideals which intersection relative annihilator ideals dual whose endpoints form x∨n x∧n respectively. For central proved P_n (S) disjunctive if only each n-ideal. Finally, discussed semi-Boolean map θ→Ker_n θ lattice isomorphism SC(S) onto K_n inverse I→θ(I) S.