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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?2012-03-28
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    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.2012-03-28
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    Btw, do I need to read about rings before moving on to modules?2012-03-28
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    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).2012-03-28
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    I like Lang's Algebra a lot.2012-03-28
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    An interesting and clear book is "Rings, Modules and Linear Algebra" by B. Hartley and T. O. Hawkes. It covers what you need to know about rings in the first three chapters. In part III it deals with the applications of module theory in linear algebra.2016-10-19

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