Algebraic Number Theory (Cambridge Studies in Advanced Mathematics, Series Number 27) - Hardcover

Fr�hlich, A.; Taylor, M. J.

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9780521366649: Algebraic Number Theory (Cambridge Studies in Advanced Mathematics, Series Number 27)

Hardcover

ISBN 10: 052136664X ISBN 13: 9780521366649

Publisher: Cambridge University Press, 1991

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This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and would-be algebraic number theorists.

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Review:

'It promises to become a classic.' Monatshefte f�r Mathematik

'... very nice and carefully written ... many excellent exercises...' European Mathematical Society Newsletter

Book Description:

Here is a thorough treatment of the foundations of algebraic number theory which is built on to introduce more advanced ideas. The systematic development of techniques for the explicit calculation of the basic invariants is emphasised throughout. They combine theory with explicit computations and applications, giving motivation in terms of classical number-theoretic problems.

"About this title" may belong to another edition of this title.