General Lattice Theory

by George Grätzer

I. First Concepts.- 1. Two Definitions of Lattices.- 2. How to Describe Lattices.- 3. Some Algebraic Concepts.- 4. Polynomials, Identities, and Inequalities.- 5. Free Lattices.- 6. Special Elements.- Further Topics and References.- Problems.- II. Distributive Lattices.- 1. Characterization Theorems and Representation Theorems.- 2. Polynomials and Freeness.- 3. Congruence Relations.- 4. Boolean Algebras R-generated by Distributive Lattices.- 5. Topological Representation.- 6. Distributive Lattices with Pseudocomplementation.- Further Topics and References.- Problems.- III. Congruences and Ideals.- 1. Weak Projectivity and Congruences.- 2. Distributive, Standard, and Neutral Elements.- 3. Distributive, Standard, and Neutral Ideals.- 4. Structure Theorems.- Further Topics and References.- Problems.- IV. Modular and Semimodular Lattices.- 1. Modular Lattices.- 2. Semimodular Lattices.- 3. Geometric Lattices.- 4. Partition Lattices.- 5. Complemented Modular Lattices.- Further Topics and References.- Problems.- V. Equational Classes of Lattices.- 1. Characterizations of Equational Classes.- 2. The Lattice of Equational Classes of Lattices.- 3. Finding Equational Bases.- 4. The Amalgamation Property.- Further Topics and References.- Problems.- VI. Free Products.- 1. Free Products of Lattices.- 2. The Structure of Free Lattices.- 3. Reduced Free Products.- 4. Hopfian Lattices.- Further Topics and References.- Problems.- Concluding Remarks.- Table of Notation.

396 pages, Paperback

First published January 1, 1978