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I would like to learn about sources that give a gentle introduction to flat modules, with exercises. Could you recommend me some source? This might be a section in a book, or some article.

I am reading the Primer in Commutative Algebra of James Milne, and I find the section on flatness harder than average in this (great) text. So I would like to find some other pedagogical source that would contain a bit more details and examples.

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I like Osborne's Basic Homological Algebra very much. Check chapter 2 for a gentle introduction to proj. / inj. & flat modules. You can find some exercises at the end of it (check in particular ex. 11, aka the "flat test lemma").

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    $\begingroup$ Thank you for this recommendation, I will have a look $\endgroup$
    – agleaner
    Apr 1, 2014 at 14:42
  • $\begingroup$ You are welcome. Also the remaining chapters are quite well written. $\endgroup$
    – Avitus
    Apr 1, 2014 at 14:43

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