A First Course in Abstract Algebra: Rings, Groups, and Fields

A textbook for a one- or two-semester course, that develops ring theory first, in order to draw upon the students' familiarity with integers and with polynomials, which are used as the motivating examples for studying rings. Coverage includes: numbers, polynomials, and factoring; rings, domains, and fields; unique factorization; permutations and group homomorphisms; constructibility problems and field extensions; and vector spaces and field extensions. Includes answers to selected exercises. Annotation copyright Book News, Inc. Portland, Or.

I was quickly won over by the book ... . The book is very complete, containing more than enough material for a two semester course in undergraduate abstract algebra ... . Even though there was a great deal of material presented, I found the book to be very well organized. ... There are a lot of things that I like about this book. ... [It is] well written and will help students to see the big picture. ... All in all it seems that a lot of thought went into this book, resulting in a comprehensive, well-written, readable book for undergraduates first learning abstract algebra.
- MAA Online

A remarkable feature of the book is that it starts first with the concept of a ring, while groups are introduced later. The reason of that is that students are usually more familiar with various number domains rather than the mappings and matrices. There is a huge number of examples in the book....The book contains a lot of nice exercises of various degrees of difficulty so that it can also be used as a practice book.
-EMS Newsletter, March 2006