This book presents modern algebra from first principles and is
accessible to undergraduates or graduates. It combines standard
materials and necessary algebraic manipulations with general concepts
that clarify meaning and importance. <P>This conceptual approach
to algebra starts with a description of algebraic structures by means of
axioms chosen to suit the examples, for instance, axioms for groups,
rings, fields, lattices, and vector spaces. This axiomatic
approach--emphasized by Hilbert and developed in Germany by Noether,
Artin, Van der Waerden, et al., in the 1920s--was popularized for the
graduate level in the 1940s and 1950s to some degree by the authors'
publication of A Survey of Modern Algebra. The present book presents the
developments from that time to the first printing of this book. This
third edition includes corrections made by the authors.

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