A Course in Universal Algebra by Stanley Neal Burris, H.P. Sankappanavar
About this book :-
This text is not intended to be encyclopedic, rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. This classic text develops the subject's most general and fundamental notions and includes examinations of Boolean algebras and model theory. The choice of topics most certainly reflects the authors' interests: Selected topics in universal algebra: an introduction to lattices, the most general and fundamental notions of universal algebra, a careful development of Boolean algebras, discriminator varieties, the introduction to some basic concepts, tools, and results of model theory. The ever-growing field of universal algebra comprises properties common to all algebraic structures, including groups, rings, fields, and lattices. A two-part treatment, it offers both an introduction and a survey of current research.
Book Detail :-
Title:
A Course in Universal Algebra by Stanley Neal Burris, H.P. Sankappanavar
Publisher:
Springer
Year:
1982
Pages:
331
Type:
PDF
Language:
English
ISBN-10 #:
0387905782
ISBN-13 #:
9780387905785
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Stanley Neal Burris
Stanley Neal Burris (born 1964) is a Distinguished Professor Emeritus and Adjunct Professor at Department of Pure Mathematics, University of Waterloo. He has completed his Ph.D. from The University of Oklahoma.
Book Contents :-
Preliminaries
Part-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
Part-II The Elements of Universal Algebra
1. Definition and Examples of Algebras
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
Part-III Selected Topics
1. Steiner Triple Systems, Squags, and Sloops
2. Quasigroups, Loops, and Latin Squares
3. Orthogonal Latin Squares
4. Finite State Acceptors
Part-IV Starting from Boolean Algebras
1. Boolean Algebras
2. Boolean Rings
3. Filters and Ideals
4. Stone Duality
5. Boolean Powers
6. Ultraproducts and Congruence-distributive Varieties
7. Primal Algebras
8. Boolean Products
9. Discriminator Varieties
10. Quasiprimal Algebras
11. Functionally Complete Algebras and Skew-free Algebras
12. Semisimple Varietie
13. Directly Representable Varieties
Part-V Connections with Model Theory
1. First-order Languages, First-order Structures, and Satisfaction
2. Reduced Products and Ultraproducts
3. Principal Congruence Formulas
4. Three Finite Basis Theorems
5. Semantic Embeddings and Undecidabilit
Recent Developments and Open Problems
1. The Commutator and the Center
2. The Classification of Varieties
3. Decidability Questions
4. Boolean Constructions
5. Structure Theory
6. Applications to Computer Science
7. Applications to Model Theory
8. Finite Basis Theorems
9. Subdirectly Irreducible Algebras
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