The Representation Of Several Important Complete Lattices

In this paper, we discuss the representation problems of several important algebraic lattices, and mainly study the representations of strongly algebraic lattices, hyperalgebraic lattices, hyperalgebraic lattices, generalized hyperalgebraic lattices andλ-hyperalgebraic lattices. We introduce the concepts of strongly regular relation,strongly finite regular relation,generalized strongly finite regular relation,λ-strongly regular relation and generalizedλ-strongly algebraic lattices, and prove that complete lattices L is strongly algebraic lattices (?) the relation≤on L is strongly regular; L is hyperalgebraic lattices (?) the relation≤on is strongly finite regular; L is generalized hyperalgebraic lattices (?) the relation≤on L is generalized strongly finite regular; L isλ-hyperalgebraic lattices (?) the relation≤on isλ-strongly regularand give their intrinsic characterizations., Besides, we also get several properties and intrinsic characterization of generalizedλ-strongly algebraic lattices, show the following result: L is generalizedλ-strongly algebraic lattices (?) L^op is ##-hyperalgebraic lattices (?)≤^OP=≥isλ-strongly regular. While, this thesis enriches the representation theory of complete lattices.