Lattices and Order

Teaching methods (Werkvormen)
28 hours lecture
28 hours tutorial

Pre-requisites (Vereiste voorkennis)
Ringen en lichamen 1

Objectives (Leerdoelen)
After this course the student is familiar with the notions of ordered algebraic structures, including lattices and Boolean algebras, and has seen the connection to various topics in algebra, analysis, and computer and information science. He or she is familiar with Formal Concept Analysis and Birkhoff Duality for finite distributive lattices, and has seen several applications including one to knowledge representation.

Contents (Beschrijving)

We will introduce lattices both as partially ordered sets and as algebras. From the partial order point of view, we treat Hasse diagrammes, complete lattices, Galois connections and Formal Concept Analysis. From the algebraic point of view, we treat the homomorphism theorems, special classes such as modular, distributive, and Boolean algebras as well as the representation theory for finite lattices and its relation to classical propositional logic.

Examination (Tentaminering)

Oral

Literature (Literatuur)
B.A. Davey & H.A. Priestley, Introduction to Lattices and Order, 2nd edn (CUP 2002).