Some Results on Semilattice
Zhu Yu-shan · Journal of Shanxi Normal University · 2006
A semilattice can be defined as a universal algebra,and it can also be defined as a partial ordered set.In this paper,we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.In order to describe the relationship between two kinds of definitions for a semilattice,we established two formulas.Moreover,we proved a necessary and sufficient condition showing the relationship between the isomorphisms of semilattices and the isomorphisms of the lattices of the ideals of the semilattices.