# Book:Stanley Burris/A Course in Universal Algebra

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Published $1981$, **Springer-Verlag Graduate Texts in Mathematics**.

The Millennium Edition can be accessed online.

### Subject Matter

### 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

- 1. Definition and Examples of Algebras

- III Selected Topics

- IV Starting from Boolean Algebras

- V Connections with Model Theory

- Recent Developments and Open Problems