The lattice structure of idempotent subsets of a semigroup
Qingde Zhang · Journal of Northeast Normal University · 2005
First is introduced the notions of interesction semilattice,intersection sublattice,union semilattice and union sublattice,and it discussed the lattice structure to several subsets of power set P(S) of a semigroup S.Based on this it proved that the all idempotent subsets of a semigroup forms a complete lattice with the ordinary subset inclusion and give a method to structure the sup and inf in the lattice.