| 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 (?) Lop is ##-hyperalgebraic lattices (?)≤OP=≥isλ-strongly regular. While, this thesis enriches the representation theory of complete lattices. |
