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I try to find some notes where is proved the equivalence between the transcendence degree and the dimension of a variety. In my course the dimension is define as the maximal lenght of ascending chain of irreducible subvarieties. Can you help me? Thank you!

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    $\begingroup$ I think this definition should be the length of a maximal chain of closed irreducible subvarieties. $\endgroup$ – Joppy Oct 12 '17 at 11:16

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