Galois Theories of Fields and Rings (Record no. 62570)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03448nam a22005175i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-58460-2 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112900.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240820s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031584602 |
| -- | 978-3-031-58460-2 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-58460-2 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA150-272 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Borceux, Francis. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 82550 |
| 245 10 - TITLE STATEMENT | |
| Title | Galois Theories of Fields and Rings |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Francis Borceux. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XII, 181 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Coimbra Mathematical Texts, |
| International Standard Serial Number | 2813-0065 ; |
| Volume/sequential designation | 2 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Historical introduction -- Part I Some Galois theorems for fields -- 1 The classical Galois theorem -- 2 The Galois theorem of Grothendieck -- 3 Profinite topological spaces -- 4 The Galois theorems in arbitrary dimension -- Part II The Galois theory of rings -- 5 Adjunctions and monads -- 6 Profinite groupoids and presheaves -- 7 The descent theory of rings -- 8 The Pierce spectrum of a ring -- 9 The Galois theorem for rings -- Further Reading -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. . |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 1501 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 65523 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 1501 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 65523 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031584596 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031584619 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031584626 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Coimbra Mathematical Texts, |
| International Standard Serial Number | 2813-0065 ; |
| Volume number/sequential designation | 2 |
| 9 (RLIN) | 82551 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-58460-2">https://doi.org/10.1007/978-3-031-58460-2</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-SXMS |
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