Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
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12 of 12 people found the following review helpful:
5.0 out of 5 stars
Crystal clear,
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This review is from: Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) (Paperback)
Samuel's book is a classic. It is a bit "antique", certainly not the most modern introduction to algebraic number theory. The topics covered in the book are algebraic and integral extensions, Dedekind rings, ideal classes and Dirichlet's unit theorem, the splitting of primes in an extension field and some Galois theory for number fields. So the range of topics is quite small (and the book is short, ~100 pages).And yet I love this book. It is crystal clear, well written and well structured; it is quite dense (especially the last chapter) and makes the beginning student of algebraic number theory think a lot, but without ever getting too heavy to digest. The list of problems is fantastic: there are many very concrete problems which sharpen your understanding of the material considerably. And last but not least, it is ridiculously cheap. I recommend this to anyone who wants to learn the basic material about number fields. Without any hesitation.
3 of 3 people found the following review helpful:
5.0 out of 5 stars
beautifully written,
By
This review is from: Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) (Paperback)
(I have read this book in French, so can't comment on the translation). This is the best introduction to number theory, and the Dover price certainly can't be beat. The one problem with this book is that the perspective is very Bourbakist, and so the arguments do not tend to be constructive, so you might want your next book to be A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)
3 of 7 people found the following review helpful:
4.0 out of 5 stars
Samuel Knows Numbers,
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This review is from: Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) (Paperback)
It's a little dense, and some proofs are lacking detail, but otherwise a great book. Extensive subject covered in one semester's worth of reading.
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