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

By A. Fröhlich,M. J. Taylor

This publication originates from graduate classes given in Cambridge and London. It offers a brisk, thorough remedy of the principles of algebraic quantity idea, and builds on that to introduce extra complicated principles. all through, the authors emphasise the systematic improvement of thoughts for the specific calculation of the elemental invariants, similar to earrings of integers, type teams, and devices. furthermore they mix, at each one level of improvement, conception with particular computations and purposes, and supply motivation by way of classical number-theoretic difficulties. a couple of distinctive issues are incorporated that may be handled at this point yet can often purely be present in study monographs or unique papers, for example: module idea of Dedekind domain names; tame and wild ramifications; Gauss sequence and Gauss classes; binary quadratic kinds; and Brauer family. this can be the one textbook at this point which mixes fresh, smooth algebraic recommendations including a considerable mathematics content material. will probably be essential for all practicing and would-be algebraic quantity theorists.

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