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Galois Theories of Fields and Rings

Name: Galois Theories of Fields and Rings
Brand: Springer, Berlin
SKU: 45303815
Price: 50.09 EUR
Availability: InStock
Author: Francis Borceux
ISBN: 9783031584596

Francis Borceux

Jazyk

Angličtina

Kniha Pevná

Libristo kód: 45303815

Nakladateľstvo Springer, Berlin, november 2023

This textbook arises from a master's course taught by the author at the University of Coimbra. It ta... Celý popis

Libristo kód: 45303815

122 b

50.09 €

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This textbook arises from a master's course taught by the author at the University of Coimbra. It takes the reader from the very classical Galois theorem for fields to its generalization to the case of rings. Given a finite-dimensional Galois extension of fields, the classical bijection between the intermediate field extensions and the subgroups of the corresponding Galois group was extended by Grothendieck as an equivalence between finite-dimensional split algebras and finite sets on which the Galois group acts. Adding further profinite topologies on the Galois group and the sets on which it acts, these two theorems become valid in arbitrary dimension. Taking advantage of the power of category theory, the second part of the book generalizes this most general Galois theorem for fields to the case of commutative rings. This book should be of interest to field theorists and ring theorists wanting to discover new techniques which make it possible to liberate Galois theory from its traditional restricted context of field theory. It should also be of great interest to category theorists who want to apply their everyday techniques to produce deep results in other domains of mathematics.