Algebraic Number Theory (Dover Books on Mathematics) by Edwin Weiss (PDF)

Description

Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate’s thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract techniques constitute the primary focus. Topics include introductory materials on elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.Subjects correspond to those usually covered in a one-semester, graduate level course in algebraic number theory, making this book ideal either for classroom use or as a stimulating series of exercises for mathematically minded individuals.

User’s Reviews

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

⭐I have used this text as a reference text and it is very good for that. It might be hard if used in a course because there are so many more readable texts in ANT.

⭐Make no mistae about it, this is a very difficult book. It is pitched at a highly advanced level and assumes a good deal of ring and field theory and makes no concessions by way of pausing to briefly summarise what is assumed at any point. Parts of the book also progress very quickly and consist of streams of definitions with next to no examples followed by a chunk of theorems that depend on the terms introduced to such an extent that the material has to be re-read many times to glean any understanding. Although in terms of the amount of material covered this is a comprehensive text, it is far too concise for student use. It might have some limited appeal as an advanced postgraduate reference book, but for anyone not already well up to speed in algebraic number theory this will be heavy going indeed.

⭐This book seems to be a good description of Algibraic valuations. Potential buyers should know that it assumes what seems to be a knowlage of graduate-level mathematics, particularly a thurogh knowlage of mathematical fields.

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