A Course in Universal Algebra by Stanley Neal Burris, H.P. Sankappanavar

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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 :-
This book has following details information.
Title: A Course in Universal Algebra by Stanley Neal Burris, H.P. Sankappanavar by NA
Publisher: Springer
Series: eBooksDirectory
Year: 1982
Pages: 331
Type: PDF
Language: English
ISBN-10 #: 0387905782
ISBN-13 #: 9780387905785
Country: Pakistan
License:
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
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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