Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates

by Robert B. Ash

This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

Genres: Mathematics, Algebra

432 pages, Paperback

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)