Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) by Pierre Samuel (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A nice short treatment of the topic. Not too hard to digest and is mostly self-contained other than the expected background material.

⭐This is a good text for a quick introduction to algebraic number theory. My poor rating has to do with this particular Dover edition. It seems that Dover did not bother to even type up the book again; they just scanned the old edition (published by Hermann), and made a new book. The pages and the binders are low quality, and the resolution on each page is bad (because it was not typed using LaTeX, they merely scanned the old version). The book is only about 100 pages, so the price for the book is not all that cheap.

⭐This book is fairly classic, but it’s pretty dense and hard to read. The typesetting is also pretty bad. You’re probably better off using one of the various good sets of online notes for algebraic number theory (J.S. Milne’s, for example). If you want a book, though, this one will do, and it’s nice and small.

⭐Accidentally bought this book twice because I forgot that I had submitted the order already. Not even mad.

⭐This is a terrific little reference book for Algebraic Number Theory. Very clear proofs and examples are provided throughout the book.

⭐An inexpensive textbook, what a dream come true! Thorough exposition, very useful.

⭐good

⭐Pros: Well written and easy to understand. Many examples. Cheap (yes, it’s form Dover.)Cons: Somewhat classical in treatment. Limited scope (no valuation theory, no local/global fields.) Printing quality is not very good (photocopied from a previously published book.)Compared with “competitors” of a similar level: Better organised than “Stewart and Tall”

⭐”Alaca and Williams”

⭐is more detailed, but some readers may find it fussy.

⭐I know it’s only $10, but whatever you do, DO NOT buy the Kindle edition of this book, the notation is horribly mutilated. I expected a higher standard of quality, but I suppose that because it’s an obscure math text few people will ever buy, Amazon does not care.

⭐L’original en français contient quelques (rares) coquilles et je m’étais donc procuré l’édition anglaise, le traducteur disant à la fin de son introduction: “These mistakes have been corrected in the present English edition”. Malheureusement, si le traducteur a corrigé certaines coquilles qui ne prêtaient pas à conséquence, il en a rajouté d’autres qui rendent parfois difficilement compréhensible le raisonnement mathématique. J’ai donc été obligé de me reporter à plusieurs reprises au texte original en français devant certaines incohérences, et bien m’en a pris. LISEZ L’ORIGINAL EN FRANçAIS!Nice

⭐If mathematics are your religion, this is your Bible.

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