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I'm looking for a reference to learn the basics of module theory for linear algebra. The purpose is to understand linear algebra in the general setting. I was reading Artin when I came across such topic, but his explanation is too brief. Can anyone give me some reference?

Thanks in advance.

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Have you looked at Dummit & Foote? –  Isaac Solomon Mar 28 '12 at 15:19
    
I remember skimming through Dummit & Foote when I started studying algebra, and immediately put it down as it seems too advanced. I'll give it a try once again. Thanks for the suggestion. –  hukr Mar 28 '12 at 15:25
    
Btw, do I need to read about rings before moving on to modules? –  hukr Mar 28 '12 at 15:47
    
Most certainly. The generalization in passing from vector spaces to modules is actually switching out the underlying field for an arbitrary ring. You should certainly have a good handle of elementary ring theory to study module theory, especially as modules generalize not only vector spaces but abelian groups and other structures that are related to rings (such as ideals). –  Isaac Solomon Mar 28 '12 at 15:55
    
I like Lang's Algebra a lot. –  Rankeya Mar 28 '12 at 17:59
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1 Answer

A very clear and elementary reference that starts from the basics is Module Theory: An Approach to Linear Algebra by T. S. Blythe. I'm not too crazy about some of the notation, particularly that dealing with dual spaces, but overall it's very informative and easy to read.

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Note also that this book is currently out-of-print but used copies can be had for a reasonable price. If you intend to acquire it, make sure you go for the second edition. The first edition is typed and not at all easy to read...the second edition has been latexed. –  ItsNotObvious Mar 28 '12 at 15:42
    
I think it's available in my school's library, I'll try to read it. –  hukr Mar 28 '12 at 15:48
    
+1 for outstanding recommendation of this classic. –  Mathemagician1234 Mar 28 '12 at 16:14
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