Book:Stanley Burris/A Course in Universal Algebra

Stanley Burris and H.P. Sankappanavar: A Course in Universal Algebra

Published $\text {1981}$, Springer-Verlag Graduate Texts in Mathematics

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