A Course in Universal Algebra

By Sankappanavar, H. P.

Book Id: WPLBN0000662277
Format Type: PDF eBook:
File Size: 1.26 MB
Reproduction Date: 2005

Title:	A Course in Universal Algebra
Author:	Sankappanavar, H. P.
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago P. Sankappanava, B. H. (n.d.). A Course in Universal Algebra. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Table of Contents
Contents Special Notation xv Preliminaries 1 I Lattices 5 x1. De nitions of Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 x2. Isomorphic Lattices, and Sublattices . . . . . . . . . . . . . . . . . . . . . . 10 x3. Distributive andModular Lattices . . . . . . . . . . . . . . . . . . . . . . . . 12 x4. Complete Lattices, Equivalence Relations, and Algebraic Lattices . . . . . . 17 x5. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 II The Elements of Universal Algebra 25 x1. De nition and Examples of Algebras . . . . . . . . . . . . . . . . . . . . . . 25 x2. Isomorphic Algebras, and Subalgebras . . . . . . . . . . . . . . . . . . . . . 31 x3. Algebraic Lattices and Subuniverses . . . . . . . . . . . . . . . . . . . . . . . 33 x4. The Irredundant Basis Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 35 x5. Congruences and Quotient Algebras . . . . . . . . . . . . . . . . . . . . . . . 38 x6. Homomorphisms and the Homomorphismand Isomorphism Theorems . . . . 47 x7. Direct Products, Factor Congruences, and Directly Indecomposable Algebras 55 x8. Subdirect Products, Subdirectly Irreducible Algebras, and Simple Algebras . 62 x9. Class Operators and Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . 66 x10. Terms, TermAlgebras, and Free Algebras . . . . . . . . . . . . . . . . . . . 68 x11. Identities, Free Algebras, and Birkho 's Theorem . . . . . . . . . . . . . . . 77 x12. Mal'cev Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 x13. The Center of an Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 x14. Equational Logic and Fully Invariant Congruences . . . . . . . . . . . . . . . 99 III Selected Topics 111 x1. Steiner Triple Systems, Squags, and Sloops . . . . . . . . . . . . . . . . . . . 111 x2. Quasigroups, Loops, and Latin Squares . . . . . . . . . . . . . . . . . . . . . 114 x3. Orthogonal Latin Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 x4. Finite State Acceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 IV Starting from Boolean Algebras : : : 129 x1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 x2. Boolean Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 x3. Filters and Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 x4. Stone Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 x5. Boolean Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 x6. Ultraproducts and Congruence-distributive Varieties . . . . . . . . . . . . . . 163 x7. Primal Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 x8. Boolean Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 x9. Discriminator Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 x10. Quasiprimal Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 x11. Functionally Complete Algebras and Skew-free Algebras . . . . . . . . . . . 199 x12. Semisimple Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 x13. Directly Representable Varieties . . . . . . . . . . . . . . . . . . . . . . . . . 212