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In Bourbaki algèbre commutative first book exercice 9 of paragraph 5 of chapter II (page 174) there is an exercise where they explain how to define the determinant of an endomorphism of a projective module of finite rank.

I'm wondering if there is a good reference for this material other than this exercise ? Not only because I would be interested in reading it but also because I want to use it in a note i'm writing and I would rather not cite an exercise.

anton
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    Google is your friend: https://projecteuclid.org/download/pdf_1/euclid.nmj/1118800587 – user26857 Jun 18 '15 at 21:02
  • Thanks a lot that will be useful ! I don't want to be annoying but I'd still be interested in a reference that uses the same approach as in Bourbaki i.e. using the definition $\det(u) = \wedge^n u$ and the fact that the endomorphism algebra of a rank 1 projective module is canonically isomorphic to the base ring (which allows one to see $\det(u)$ as an element of the base ring). – anton Jun 18 '15 at 21:44

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