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This Second Edition of "one of the best books available to support a one-semester introduction to abstract algebra" ( CHOICE ) presents pivotal ideas in the evolution of algebra and provides readers with the opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. Including four new appendices and over 1,000 new examples and multi-level exercises, it features new sections covering rings and fields, group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, the fundamental theorem of algebra, plus more.