Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates

by Robert B. Ash

Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible.The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.

Genres: Mathematics, Algebra

611 pages, Kindle Edition

First published January 1, 2006

About the author

Professor Emeritus, Mathematics
University of Illinois at Urbana-Champaign

Reviews

[Nikolay Zakirov · Rating 4 out of 5]

It is a pretty good book. Intuitive story-telling and problems with solutions are its strong parts. However, I think it could be further improved. The weak part is a lot of "long distance" links in the proofs. E.g. take 6.1.2. proposition in the Galois theory section. It states some properties of fixed fields. The proof is as short as a few lines. However, in the proof there are references to propositions 3.4.7, 3.5.8., 3.5.9, 3.1.9 - all from different parts of section 3, not on the same page. Many of these references could be supplemented by a short few-words description of what they refer to right in the proof so that a knowledgeable reader would not have to go and open section 3 at all. These "long distance" references without any description slow down reading.
(I was reading a pdf version of the text from the screen)