Algebraic Number Theory (Cambridge Studies in Advanced by A. Fröhlich,M. J. Taylor PDF

By A. Fröhlich,M. J. Taylor

This e-book originates from graduate classes given in Cambridge and London. It presents a brisk, thorough therapy of the rules of algebraic quantity conception, and builds on that to introduce extra complex rules. all through, the authors emphasise the systematic improvement of suggestions for the categorical calculation of the fundamental invariants, equivalent to earrings of integers, type teams, and devices. in addition they mix, at every one level of improvement, conception with particular computations and purposes, and supply motivation by way of classical number-theoretic difficulties. a few specified themes are integrated that may be taken care of at this point yet can often in basic terms be present in examine monographs or unique papers, for example: module idea of Dedekind domain names; tame and wild ramifications; Gauss sequence and Gauss sessions; binary quadratic types; and Brauer family. this is often the single textbook at this point which mixes fresh, sleek algebraic concepts including a considerable mathematics content material. will probably be imperative for all practicing and would-be algebraic quantity theorists.

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