Abstract algebra : A Comprehensive Treatment

An ambitious, comprehensive book covering subject matter typically taught over the course of two or three years, Abstract Algebra offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to automatically smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe.Including an original treatment of representation of finite groups that avoids the use of semisimple ring theory, Abstract Algebra explains sets, maps, posets, lattices, and other essentials of the algebraic language...Peano's axioms and cardinality...groupoids, semigroups, monoids, groups, and normal subgroups...congruences and isomorphism theorems for groups...cyclic groups and the symmetric group...Sylow's theorems...rings, ideals, homomorphisms, and quotient rings...unique factorization and principal ideal and Euclidean domains...quotient fields and the factoriality of rings of polynomials...modules and vector spaces...Galois theory...linear codes...and ordered rings.