Universal Algebra: Fundamentals and Selected Topics

FUNDAMENTALS OF UNIVERSAL ALGEBRA Algebras Operations Examples More about subs, homs, and prods Generating subalgebras Congruences and quotient algebras Lattices Ordered sets Distributive and modular lattices Complete lattices Closure operators and algebraic lattices Galois connections Ideals in lattices The Nuts and Bolts of Universal Algebra The isomorphism theorems Direct products Subdirect products Case studies Varieties and other classes of algebras Clones, Terms, and Equational Classes Clones Invariant relations Terms and free algebras Identities and Birkhoff's theorem The lattice of subvarieties Equational theories and fully invariant congruences Maltsev conditions Interpretations SELECTED TOPICS Congruence Distributive Varieties Ultrafilters and ultraproducts Jonsson's lemma Model theory Finitely based and nonfinitely based algebras Definable principal (sub)congruences Arithmetical Varieties Large clones How rare are primal algebras? Maltsev Varieties Directly representable varieties The centralizer congruence Abelian varieties Commutators Directly representable varieties revisited Minimal varieties Functionally complete algebras Finite Algebras and Locally Finite Varieties Minimal algebras Localization and induced algebras Centralizers again! Applications Bibliography Index