Groups, Rings, Modules (Dover Books on Mathematics)

By: Maurice Auslander and David Buchsbaum

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Synopsis: This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions and Dedekind domains. Exercises are provided at the end of each chapter.