I am searching for a self-contained book in Algebra that I can use as a reference while studying more advanced topics in Algebraic Number Theory (like Class Field Theory).

I have taken an introduction course in Galois Theory, a more advanced course in Commutative Algebra (Atiyah and MacDonald) and a course in Number Theory (where we used a book by D. Marcus called Number Fields).

My main interest is in Algebraic Number Theory and currently I have started to read the book by Neukirch called Algebraic Number Theory.

Best regards, Sigve

  • $\begingroup$ For reference you can take whatever fits you better, and with the stuff you've already studied I think you;re the best to decide what is, or what are, the best references. $\endgroup$ – DonAntonio Dec 15 '17 at 15:37
  • $\begingroup$ I would suggest Daniel Marcus' "Number Fields", which leads you to the threshold of CFT. Its non negligible asset is to contain a tremendous mine of (interesting) exercises. $\endgroup$ – nguyen quang do Dec 16 '17 at 14:49

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