Book:Stanley Burris/A Course in Universal Algebra

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

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

The Millennium Edition can be accessed online.

Subject Matter


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
Semigroups and Monoids
Quasigroups and Loops
Modules Over a (Fixed) Ring
Algebras Over a Ring
Bounded Lattices
Boolean Algebras
Heyting Algebras
n-Valued Post Algebras
Cylindric Algebras of Dimension n
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