lattice homomorphism
4.It is demonstrated that the Cartesian product and the subalgebra of completely distributive lattices are still a completely distributive lattice, and the image of the completely distributive lattices under a surjective homomorphism is also a completely distributive lattice. Finally, an important conclusion on quotients is reached with a similar conclusion arrived at for meet continuous lattices.
5.In this paper, it is shown that the mapping ρ|?ctr ρ is a complete homomorphism of the strong P congruence lattice of S(P) onto the lattice of normal equivalences on P , and that the congruence θ induced by it has all its classes complete modular lattices.
6.For every fuzzy lattice and noempty set X, the existence of minimal LF T_2 topoiogy on L~x is proved and the structure of this kind of topology is discussed with the aid of some tools such as order-homomorphism, Ideal,etc.
7.It is shown that if Clifford semigroup S=[Y;G_α,φ_(α,β)] is subdirectly irreducible,then the structure homomorphism φ_(α,β)(α≥β) is injective and Y is a lattice that have at most two elements.
