Books on module theory for linear algebra 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.
 A: 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!

Download the book here!
A: 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.
