Basic Algebra

Cornerstones, Birkhäuser, Boston, 2006. 
ISBN: 0-8176-3248-4.
717+xxii pages.

A second printing, identical to the above version on the outside, appeared in 2015 with a great many changes.  It is close in content to the digital second edition.  A discussion of the differences between the digital second edition and the second printing of the first edition may be found here.

A companion volume Advanced Algebra was published in 2007.
ISBN: 0-8176-4522-5.

ISBN: 0-8176-4533-0 for the two-volume set, Basic Algebra and Advanced Algebra.

Chapter Titles:

Preliminaries about the Integers, Polynomials, and Matrices
Vector Spaces over Q, R, and C
Inner-Product Spaces
Groups and Group Actions
Theory of a Single Linear Transformation
Multilinear Algebra
Advanced Group Theory
Commutative Rings and Their Modules
Fields and Galois Theory
Modules over Noncommutative Rings
Appendix: Background Topics

Files Available:

Table of Contents - PDF
Preface, Dependence Among Chapters, Guide for the Reader - PDF
Index - PDF


The final list of corrections to the 2006 version appears in the file below.  Many of the corrections were kindly sent to the author by Skip Garibaldi of Emory University and Ario Contact of Shiraz, Iran.  The long correction for pages 596-598 resulted from a discussion with Qiu Ruyue.

Final list of corrections (11/5/2015) - PDF

Last modified: 3/11/2016