I originally learned algebraic number theory from Marcus's Number Fields book and think it is a wonderful book. Unfortunately, almost every proof leaves at least one unproved statement to the reader. Sometimes, I want to go back and quickly review a proof of a theorem without the burden of reinventing proofs. Can anyone suggest some other algebraic number theory books at a similar level to Marcus that genuinely have complete proofs of the theorems?

Thanks, Alan

  • $\begingroup$ Neukrich, Lang, Hecke $\endgroup$ – reuns Feb 14 at 0:14
  • $\begingroup$ Thanks for the suggestions. I have a copy of Neukirch and it is like Marcus until page 65 when he starts treating everything locally which is a totally different way of thinking about the topic. Lang goes local by page 22 and is not similar to Marcus either. I spent hundreds of hours studying Lang's Algebraic Number Theory in grad school because my advisor told me to, but Lang's clarity is so poor that it was mostly a waste of time. I'll see if I can find Hecke in the library. $\endgroup$ – Alan C. Feb 14 at 2:18
  • $\begingroup$ I personally like Alaca & Williams, Introductory Algebraic Number Theory, even though I have yet to read the whole book. $\endgroup$ – Robert Soupe Feb 14 at 2:41
  • $\begingroup$ Robert, I actually taught a course using Alaca and Williams a few years ago. It was quite a nice book. It had a good mix of theory and examples. I used it for a graduate course but decided it was just a little lower than the level of our students at BYU and so chose Marcus this time because I thought it would be at a more appropriate level. I'm finding preparation for class a little more time consuming than I had expected. $\endgroup$ – Alan C. Feb 14 at 2:54

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