Algebra (Ams Chelsea Publishing) （3RD）

Lane, Saunders Mac/ Birkhoff, Garrett

American Mathematical Society（1988/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 626 p.
• 言語 ENG
• 商品コード 9781470474768

Full 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.

Contents

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