Galois Theories of Fields and Rings

Name: Galois Theories of Fields and Rings
Brand: Springer
SKU: 9783031584626
Price: 4404.0 INR
Availability: InStock

by Francis Borceux

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ISBN13: 9783031584626
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: January 1, 2024
Pages: 193
Original Price: EUR 59.94
Language: English
Edition: N/A
Item Weight: 286 grams
BISAC Subject(s): Algebra / General

About The Book

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.

About The Author

Francis Borceux is a category theorist at the University of Louvain, Belgium. He has developed research in algebra and essentially taught geometry, number theory, and algebra courses.

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