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I need some good reference for studying valuations, I was looking for some really detailed material, as I'm just starting to study this theme. Please help.

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    $\begingroup$ This is covered in almost all books on algebraic number theory or commutative algebra. I think the best is to have a look at some books on algebraic number theory in general. The chapters surrounding valuations could be even more helpful than studying valuations alone. $\endgroup$ – Dietrich Burde Mar 18 at 19:12
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Chapters 5,9 and 10 of Atiyah--Macdonald are a good algebraic reference http://www.math.toronto.edu/jcarlson/A--M.pdf

But as a number theorist I prefer Chapter II of Neukirch https://www.cimat.mx/~luis/seminarios/Teoria-de-Numeros/Neukirch_Algebraic_number_theory.pdf

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Most books on Commutative Algebra should cover the basics, for example "Introduction to Commutative Algebra" by Atiyah and MacDonald, or "Commutative Ring theory" by Matsumura (not to be confused with his older book "Commutative Algebra").

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