Lattices and Ordered Sets

• Main Author: Roman, Steven (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2008.
• Subjects: Mathematics.; Algebra.; Ordered algebraic structures.; Order, Lattices, Ordered Algebraic Structures.

This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in ab...

Table of Contents:

• Basic Theory
• Partially Ordered Sets
• Well-Ordered Sets
• Lattices
• Modular and Distributive Lattices
• Boolean Algebras
• The Representation of Distributive Lattices
• Algebraic Lattices
• Prime and Maximal Ideals; Separation Theorems
• Congruence Relations on Lattices
• Topics
• Duality for Distributive Lattices: The Priestley Topology
• Free Lattices
• Fixed-Point Theorems.