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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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  • $\begingroup$ Have you looked at Dummit & Foote? $\endgroup$
    – Elchanan Solomon
    Mar 28, 2012 at 15:19
  • $\begingroup$ 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. $\endgroup$
    – hukr
    Mar 28, 2012 at 15:25
  • $\begingroup$ Btw, do I need to read about rings before moving on to modules? $\endgroup$
    – hukr
    Mar 28, 2012 at 15:47
  • $\begingroup$ 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). $\endgroup$
    – Elchanan Solomon
    Mar 28, 2012 at 15:55
  • $\begingroup$ I like Lang's Algebra a lot. $\endgroup$
    – Rankeya
    Mar 28, 2012 at 17:59

2 Answers 2

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As it was suggested before, Module Theory: An Approach to Linear Algebra by T. S. Blyth is an awesome title which covers almost every basic topic of Module theory in a very elegant, clear and efficient way. It is hands down my favorite text in the subject, but unfortunately it has been long out of print and therefore it is expensive and hard to obtain.

I contacted T. S. Blyth a few months ago looking for the possibility of a new edition, or at least, for a Dover reprint or something like that. Recently, Tom told me that he just finished an electronic edition, and I inmediately helped him with a careful and exhausting typo hunting. With great joy, I shall let you all know that this venerable text is now available for free!

http://hdl.handle.net/10023/12643 Download the book here!

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    $\begingroup$ Normally I wouldn't upvote an answer to a five year old question which recommends the same book as the sole existing answer. But this is an exceptional case, kudos! $\endgroup$
    – pjs36
    Feb 4, 2018 at 1:07
  • $\begingroup$ Just a note that the download link goes to research-repository.st-andrews.ac.uk/handle/10023/12643 (St Andrews Research Repository) $\endgroup$
    – J W
    Feb 6, 2021 at 15:14
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A very clear and elementary reference that starts from the basics is Module Theory: An Approach to Linear Algebra by T. S. Blyth. 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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    $\begingroup$ 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. $\endgroup$
    – ItsNotObvious
    Mar 28, 2012 at 15:42
  • $\begingroup$ I think it's available in my school's library, I'll try to read it. $\endgroup$
    – hukr
    Mar 28, 2012 at 15:48

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