Can anyone recommend an easy to read algebraic number theory book?

Question

Can anyone recommend an easy to read algebraic number theory book?

I prefer a book with good examples. (Hints or answers to selected questions, if possible. Not sure if it is possible for a book of this topic.)

Answer 1

The problem with most algebraic number theory texts is that they assume you already have a good grounding in advanced algebra topics like isomorphisms, bijections, mappings, etc. Maybe you did good in high school algebra, doing stuff like solving an equation with one variable or finding the slope of a line. That's vital but basic.

With that in mind, I recommend the Dover reprint of Ethan Bolker's Elementary Number Theory: An Algebraic Approach. It is an old text with a long errata, but it's very readable and makes a lot of sense even if you can't tell a field monomorphism from a field coil. If you read Bolker's book, you might be better prepared to understand a book like Introductory Algebraic Number Theory by Alaca and Williams.

Topics in Commutative Ring Theory by John Watkins is not quite what you're asking for, but it does have answers to selected exercises.

Answer 2

Algebraic Number Theory by Frazer Jarvis has numerous examples and exercises, with answers in an appendix, and is aimed at undergraduates. The author recommends background in elementary number theory, linear algebra, a little group theory (up to Lagrange's theorem) and some familiarity with rings and fields. Ideals and quotient rings are taught in the book.

A recent alternative that's very gentle indeed is Stillwell's Algebraic Number Theory for Beginners: Following a Path from Euclid to Noether. The required background is minimal - even the requisite linear algebra is covered in the book. (Publisher's webpage here.)