Date of Publication
10-1992
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Algebra | Algebraic Geometry | Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Aurora S. Trance
Defense Panel Chair
Blessilda Raposa
Defense Panel Member
Severino Diesto
Arlene Pascasio
Abstract/Summary
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.
Abstract Format
html
Language
English
Format
Accession Number
TG02070
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
118 leaves, 28 cm.
Keywords
Partitions (Mathematics); Congruences and residues; Lattices; distributive; Numbers, Theory of
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Recommended Citation
Sia, L. O. (1992). Partitions, congruence relations and simple lattices. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1440
