Abstract Algebra: An Integrated Approach

by Joseph H. Silverman

This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.

567 pages, Paperback

Published March 6, 2022

Reviews

[Pat · Rating 5 out of 5]

really liked the "integrated approach" part of the book! first semester we covered groups pt. 1, rings pt. 1, and fields pt. 1, and then groups pt. 2, rings pt. 2, and fields pt. 2; second semester was galois theory, module theory, and the section on elliptic curves (haven't looked at groups pt. 3 or the other extra topics in ch. 14 yet).

lots of good exposition and the material is presented very nicely.

[MM Kh · Rating 5 out of 5]

This book reads extremely well and is a great choice for self-study, in my experience. What makes this book appealing to my taste is that it covers groups, rings, and fields at a broad level first and then covers them in more detail later in the book. This way, a person curious about these concepts will get an idea rather soon in the book (as opposed to other algebra books that tend to cover each of these topics in sequential order, leaving, for example, fields 200 pages deep in the book).

Overall, I like the style of this book, and I think it is well-suited for self-study.