Book:Stanley Burris/A Course in Universal Algebra

The Millennium Edition can be accessed online.

Subject Matter

 * Universal Algebra

Contents

 * Preface


 * I Lattices
 * 1. Definitions of Lattices
 * 2. Isomorphic Lattices, and Sublattices
 * 3. Distributive and Modular Lattices
 * 4. Complete Lattices, Equivalence Relations, and Algebraic Lattices
 * 5. Closure Operators


 * II The Elements of Universal Algebra
 * 1. Definition and Examples of Algebras
 * Groups
 * Semigroups and Monoids
 * Quasigroups and Loops
 * Rings
 * Modules Over a (Fixed) Ring
 * Algebras Over a Ring
 * Semilattices
 * Lattices
 * Bounded Lattices
 * Boolean Algebras
 * Heyting Algebras
 * n-Valued Post Algebras
 * Cylindric Algebras of Dimension n
 * Ortholattices
 * 2. Isomorphic Algebras, and Subalgebras
 * 3. Algebraic Lattices and Subuniverses
 * 4. The Irredundant Basis Theorem
 * 5. Congruences and Quotient Algebras
 * 6. Homomorphisms and the Homomorphism and Isomorphism Theorems
 * 7. Direct Products, Factor Congruences, and Directly Indecomposable Algebras
 * 8. Subdirect Products, Subdirectly Irreducible Algebras, and Simple Algebras
 * 9. Class Operators and Varieties
 * 10. Terms, Term Algebras, and Free Algebras
 * 11. Identities, Free Algebras, and Birkhoff’s Theorem
 * 12. Mal’cev Conditions
 * 13. The Center of an Algebra
 * 14. Equational Logic and Fully Invariant Congruences


 * III Selected Topics


 * IV Starting from Boolean Algebras


 * V Connections with Model Theory


 * Recent Developments and Open Problems