I'd like to learn some number theory, since it provides a lot of motivation for commutative ring theory and even some motivation for lattice theory (at least, that's the impression I'm under). Therefore, I'm looking for a number-theory book that develops and/or makes heavy use of commutative ring theory and lattice theory, but which is reasonably elementary (I am a finishing bachelor's student i.e. undergrad) and suitable for self-learning.

Any recommendations?

  • $\begingroup$ Pierre Samuel's Algebraic theory of Numbers should be a good option, I think. $\endgroup$ – user119882 Apr 24 '14 at 9:49

I would highly recommend Lorenzini's text Introduction to Arithmetic Geometry. It gives a very good, very intuitive, and very thorough introduction to the basics of algebraic number theory, and plane algebraic geometry, highlighting the similarities between the two.

It sounds perfect for what you're after.


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