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What is the prerequisite knowledge for learning Galois theory? I don't know what a ring is.

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Start by learning what a ring is, then. You also need to know about groups and fields. –  Zhen Lin Jun 2 '12 at 11:26
Ideally, one would have the basics of linear algebra, groups, rings and fields down. All of those mix into the pot when you do Galois theory. –  Ragib Zaman Jun 2 '12 at 11:37
Perhaps you could tell us about what abstract algebra you do know? –  Dylan Moreland Jun 2 '12 at 11:39

3 Answers 3

up vote 8 down vote accepted

If you don't know a great deal of abstract algebra so far, maybe "A First Course in Abstract Algebra" by Fraleigh might be a good place to start, as it includes all the prerequisites (groups, rings, fields, linear algebra) as well as a very readable treatment of Galois Theory itself.

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Try also these excellent books:

and also

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Good references.Thanks. –  awllower Jun 2 '12 at 15:48

Read this book, as a first step.
Summing over the comments below, one could conclude that a necessary prerequisite is the collection of such theories as groups, rings, fields, and linear algebra. Of course it needs to know what a field is, and what a group is, before you learn Galois theory; also, it appears almost everywhere the use of linear algebra. In fact, I think those should suffice for a first-time exposition to the theory. Indeed, familiarity grows with time one spends in practicing the theory.

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It is little but complete, detailed but fluent, and classical in some sense. –  awllower Jun 2 '12 at 11:32
So, in order to learn the theory, it needs and it suffices to have in mind some knowledge about groups. It should enable you to understand what the book is talking about, in most cases. –  awllower Jun 2 '12 at 11:34
I don't think Rotman's book is a good place to start Galois Theory from scratch: it assumes, as most book on the subject do, that you already know linear algebra and basic group and ring theory, without which you will have a very hard time understanding the theory. –  DonAntonio Jun 2 '12 at 12:07
Rotman's book is nice if you have some prerequisites down (basic group theory, rings, fields, polynomials etc). As he says, the treatment of these things is "not leisurely, but it is complete", so it's more like a review of things you already are somewhat familiar with. Also if you use this book, make sure to get the second edition because the first edition is full of mistakes. The second edition still has a few mistakes in it, and has a bit incoherent structure sometimes (using terms that are defined later in the book, etc.). But I think it's a nice introduction. –  Mikko Korhonen Jun 2 '12 at 14:37

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