
Algebra
American Mathematical Society (Publisher)
3rd Edition
Published on 31. January 1988
Book
Paperback/Softback
626 pages
978-1-4704-7476-8 (ISBN)
Description
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.
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.
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.
Reviews / Votes
"Nearly every ten years there seems to arrive a new edition of this now classical book the review of which the reviewer hardly can improve. The main advantage of the authors had been the introduction of thoroughly categorical concepts into algebra." - Zentralblatt MATH"The book is clearly written, beautifully organized, and has an excellent and wide-ranging supply of exercises ... contains ample material for a full-year course on modern algebra at the undergraduate level." - Mathematical Reviews
More details
Series
Edition
Third Edition
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Edition type
New edition
ISBN-13
978-1-4704-7476-8 (9781470474768)
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Schweitzer Classification
Content
Sets, functions, and integers
Groups
Rings
Universal constructions
Modules
Vector spaces
Matrices
Special fields
Determinants and tensor products
Bilinear and quadratic forms
Similar matrices and finite abelian groups
Structure of groups
Galois theory
Lattices
Categories and adjoint functors
Multilinear algebra
Appendix: Affine and projective spaces
Bibliography
Index
Groups
Rings
Universal constructions
Modules
Vector spaces
Matrices
Special fields
Determinants and tensor products
Bilinear and quadratic forms
Similar matrices and finite abelian groups
Structure of groups
Galois theory
Lattices
Categories and adjoint functors
Multilinear algebra
Appendix: Affine and projective spaces
Bibliography
Index