Partitions, congruence relations and simple lattices

• Main Author: Sia, Lucy O.
• Format: text
• Language: English
• Published: Animo Repository 1992
• Subjects: Partitions (Mathematics); Congruences and residues; Lattices; distributive; Numbers, Theory of; Algebra; Algebraic Geometry; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1440; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8278/viewcontent/TG02070_F_Redacted.pdf
• Institution: De La Salle University

This study investigates the relation between partition of a lattice into convex sublattices and the congruence relation on the lattice. Properties of simple lattices and their use in characterizing the structure of a lattice are discussed. Specifically, it focuses primarily on the simple lattice and its properties and then provides a simplified but detailed proof of a general structure theorem by R.P. Dilworth which is found in Dilworth, R. P. The Structure of Relatively Complemented Lattices, Annals of Mathematics, 51, No. 2(1950), stated as follows: L is a direct product of a finite number of lattices if and only if the distributive lattice (L) of all congruence relations on L is a finite Boolean algebra in which all elements permute.