Post-Modern AlgebraAdvanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work. |
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A₁ A₂ abelian group action adjunction algebraic theory automorphism b₁ bijection binary C₁ called coequalizer comma category commutative component composite congruence Consider coproduct Corollary d₁ Define denote Determine diagonal diagram disjoint union equation equivalence relation Example Exercise finite forgetful functor free monoid functor F G-set given group G group homomorphism ideal initial object injects integral domain inverse property Isomorphism Theorem K-algebra lattice left adjoint Let F Let G linear loop transversal M-set M-subset matrix module monad monoid homomorphism morphism Moufang multiplication multiset natural number natural transformation non-zero notation Note operation parallel pair permutation phism polynomial poset positive integer prevariety Proof Proposition Prove quasigroup right adjoint right S-module Section semigroup semilattice Show slice category small category structure subalgebra subcategory subgroup submonoid subset surjects terminal object unique unital ring Verify x₁ yields