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The out-of-print book is Commutative Algebra by Matsumura. For example, you can't buy it on Amazon.

I take notes, solve the exercises, but sometimes in my notes (typed) I just copy word-for-word what is written.

If posting the notes in chunks in a blog format is illegal, what is the best I can do? For example offer a download with PDF. I am not deriving any money from this, just wanting to share my notes to anyone who finds them useful.

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    Depends on your jurisdiction and how extensive you quote. If you make the quotes explicit, your local laws might allow quoting the text.
    – Polygnome
    Oct 17 '20 at 20:59
  • @Polygnome United States Oct 17 '20 at 21:00
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    Out of print means nothing when it comes to copyright: copyright.gov/help/faq/faq-duration.html Oct 17 '20 at 21:04
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    @CommutativeAlgebraStudent by using quotation marks (e.g. " or guillemets) and stating the source. Also, see janefriedman.com/sample-permission-letter
    – Polygnome
    Oct 17 '20 at 21:06
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    It is often not that big a deal to get permission from the author for something like that. Authors don't have a financial stake is the sales of out of print books which are a minor source of income anyway, and are usually more motivated to get people to use and understand their textbooks for prestige purposes.
    – ohwilleke
    Oct 19 '20 at 23:33

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