Algebra

8vo (24 cm), XIX, [1], 598 pp. Publisher's cloth (minor shelf wear). Third edition. This book presents modern algebra from first principles and is suitable for both undergraduates and graduate students. It integrates standard material and essential algebraic techniques with general concepts that clarify their meaning and significance. The conceptual approach to algebra begins with a description of algebraic structures using axioms tailored to fit specific examples, such as those for groups, rings, fields, lattices, and vector spaces. This axiomatic approach, emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, and others in the 1920s, was popularized for graduate-level study in the 1940s and 1950s, in part through the authors' publication of A Survey of Modern Algebra. Since that time, algebra has expanded vigorously; this book is also designed to present the basic new concepts that have appeared.