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Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).

The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.

Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).

So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, ...

Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).

Thanks in advance!

  • 0
    Someone has to say Lang! Just kidding though, that's not a good book for study, though the problems are nice. I'm not in love with any algebra book out there. Maybe I should write one? I learned from Lang, Artin, Rotman, etc. Exposing yourself to a variety of views is a good idea.2016-02-26

10 Answers 10

28

There's always the classic Abstract Algebra by Dummit and Foote. Section II of the text gives a nice treatment of ring theory, certainly providing plenty of review for what you have already covered while introducing more advanced concepts of ring theory. Section III will cover the field and Galois theory you're interested in. Some of the exercises can be difficult at times, especially for self-study, but the authors tend to give a number of examples and always provide the motivation for why they are doing what they are doing.

  • 0
    There is nothing classic about D&F .2017-12-14
19

Fraleigh's "A First Course in Abstract Algebra, 7th Edition" is a good book for self study. It is easy and good for the beginners, and it has a complete solution manual written by the author.

13

Try Contemporary Abstract Algebra. This one, I think, has lots of nice examples. The following is from Googlebooks:

"Contemporary Abstract Algebra 7/e provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students."

Also, I would like to suggest you read this article in wikipedia. You may find the references valuable.

8

I learned abstract algebra from Rotman's "First Course in Abstract Algebra". His expository style is easy to follow and the exercises he gives are helpful.

  • 2
    +1 for Rotman. ANYTHING by Rotman claiming to be a textbook is outstanding in my experience!2011-11-25
8

Note: This answer is copied over from an answer I gave on a previous very-similar question, because it still applies here.

This is likely not going to be a popular suggestion, since it's relatively unknown, but I think the perfect book for you is Allan Clark's Elements of Abstract Algebra.

It's a unique book that covers the basics of group theory, ring theory, and even a tiny bit of Galois Theory, but it does it almost entirely through problems. Every chapter begins with a short section defining some terms and giving a few basic proofs, and then it leads the reader through the rest of the exposition in a series of problems, some difficult, some not. The end result is that if you actually do all the problems, you've written the book yourself. It's impossible not to be comfortable with basic abstract algebra if you take this book seriously.

It's also probably the cheapest book on this entire list :)

  • 0
    I love that book!2016-02-26
5

It depends on which subject you’re interested in particular. Here is a list of the books if find go in the greatest depth and yield the clearest intuition on each major subject:


Familiar Structures:


Abstract Structures:

3

My suggestions are 1) Fraleigh 2) Gallian 3) Herstein and 4) Rotman,

  • 2
    I've corrected *Rotoman* to *Rotman* - I suppose it was a typo. (I do not know about a book on algebra by Rotoman, neither does [Google](https://www.google.com/search?q=Rotoman+algebra).)2013-07-02
3

I am speaking from the standpoint of a student, and I think that a very good book on introductory abstract algebra that doesn't get mentioned very often is Basic Algebra by Anthony W. Knapp. From experience, the text is accessible with very little pre-requisite knowledge, is less "talkative" than Dummit and Foote (and in my opinion, definitely not dry, unlike D&F), and more rigorous in exposition than Artin's Algebra, although Artin's book is a good and standard first text as well.

Knapp covers most basic topics that the undergraduate student needs to know and is largely self-contained. I think, for the first seven chapters of this book, you can't really do much better by way of alternative texts. However, you could supplement or even replace the eighth chapter with Introduction to Commutative Algebra by Michael Atiyah and Ian MacDonald. However, if you are reading algebra for the first time, I don't suggest using Atiyah's book, unless you are feeling very confident or very lucky! :) Having said that, it is an excellent book and you should try reading it at some point. For the ninth chapter, you could use Emil Artin's classic little book on Galois Theory, based on his lectures on the subject. Another good reference which I haven't used but heard quite a few good things about is Nathanson's Basic Algebra: I (Chapter 4 (?), I think). Yet another book on Galois Theory is D.J.H. Garling's Galois Theory, which is where I initially learnt my Galois Theory from. As for Chapter 10 in Knapp, I have nothing to say, since I never got down to reading it.

2

Fundamentals of Abstract Algebra by Malik, Sen & Mordeson is a very good book for self study.The topics are covered in detail with many interesting examples and exercises.Also it provides hints and answers to difficult questions making it suitable for self study.