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.
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Algebra
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Table of contents
- Front Cover
- Preface to the Third Edition
- From the Preface to the First Edition
- From the Preface to the Second Edition
- Contents
- List of Symbols
- CHAPTER I Sets, Functions, and Integers
- CHAPTER II Groups
- CHAPTER III Rings
- CHAPTER IV Universal Constructions
- CHAPTER V Modules
- CHAPTER VI Vector Spaces
- CHAPTER VII Matrices
- CHAPTER VIII Special Fields
- CHAPTER IX Determinants and Tensor Products
- CHAPTER X Bilinear and Quadratic Forms
- CHAPTER XI Similar Matrices and Finite Abelian Groups
- CHAPTER XII Structure of Groups
- CHAPTER XIII Galois Theory
- CHAPTER XIV Lattices
- CHAPTER XV Categories and Adjoint Functors
- CHAPTER XVI Multilinear Algebra
- APPENDIX Affine and Projective Spaces
- Bibliography
- Index To the Appendix
- Index
- Back Cover
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Yes, you can access Algebra by Saunders Mac Lane,Garrett Birkhoff in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.