Topological Galois theory: solvability and unsolvability of equations in finite terms
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2014
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783642388705 9783642388712 |
| DOI: | 10.1007/978-3-642-38871-2 |
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Record in the Search Index
| _version_ | 1804152726461874176 |
|---|---|
| adam_text | TOPOLOGICAL GALOIS THEORY
/ KHOVANSKII, ASKOLD
: 2014
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
1 CONSTRUCTION OF LIOUVILLIAN CLASSES OF FUNCTIONS AND LIOUVILLE’S
THEORY
2 SOLVABILITY OF ALGEBRAIC EQUATIONS BY RADICALS AND GALOIS THEORY
3 SOLVABILITY AND PICARD–VESSIOT THEORY
4 COVERINGS AND GALOIS THEORY
5 ONE-DIMENSIONAL TOPOLOGICAL GALOIS THEORY
6 SOLVABILITY OF FUCHSIAN EQUATIONS
7 MULTIDIMENSIONAL TOPOLOGICAL GALOIS THEORY
APPENDIX A: STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
APPENDIX B: CHEBYSHEV POLYNOMIALS AND THEIR INVERSES
APPENDIX C: SIGNATURES OF BRANCHED COVERINGS AND SOLVABILITY IN
QUADRATURES
APPENDIX D: ON AN ALGEBRAIC VERSION OF HILBERT’S 13TH PROBLEM
REFERENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
TOPOLOGICAL GALOIS THEORY
/ KHOVANSKII, ASKOLD
: 2014
ABSTRACT / INHALTSTEXT
THIS BOOK PROVIDES A DETAILED AND LARGELY SELF-CONTAINED DESCRIPTION OF
VARIOUS CLASSICAL AND NEW RESULTS ON SOLVABILITY AND UNSOLVABILITY OF
EQUATIONS IN EXPLICIT FORM. IN PARTICULAR, IT OFFERS A COMPLETE
EXPOSITION OF THE RELATIVELY NEW AREA OF TOPOLOGICAL GALOIS THEORY,
INITIATED BY THE AUTHOR. APPLICATIONS OF GALOIS THEORY TO SOLVABILITY OF
ALGEBRAIC EQUATIONS BY RADICALS, BASICS OF PICARD–VESSIOT THEORY, AND
LIOUVILLE S RESULTS ON THE CLASS OF FUNCTIONS REPRESENTABLE BY
QUADRATURES ARE ALSO DISCUSSED. A UNIQUE FEATURE OF THIS BOOK IS THAT
RECENT RESULTS ARE PRESENTED IN THE SAME ELEMENTARY MANNER AS CLASSICAL
GALOIS THEORY, WHICH WILL MAKE THE BOOK USEFUL AND INTERESTING TO
READERS WITH VARIED BACKGROUNDS IN MATHEMATICS, FROM UNDERGRADUATE
STUDENTS TO RESEARCHERS. IN THIS ENGLISH-LANGUAGE EDITION, EXTRA
MATERIAL HAS BEEN ADDED (APPENDICES A–D), THE LAST TWO OF WHICH WERE
WRITTEN JOINTLY WITH YURA BURDA
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Chovanskij, Askolʹd G. 1947- |
| author_GND | (DE-588)1064596754 |
| author_facet | Chovanskij, Askolʹd G. 1947- |
| author_role | aut |
| author_sort | Chovanskij, Askolʹd G. 1947- |
| author_variant | a g c ag agc |
| building | Verbundindex |
| bvnumber | BV042206297 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)894703190 (DE-599)DNB1059337010 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-38871-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:15:18Z |
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| spelling | Chovanskij, Askolʹd G. 1947- Verfasser (DE-588)1064596754 aut Topological Galois theory solvability and unsolvability of equations in finite terms Askold Khovanskii Berlin [u.a.] Springer 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics Topologische Methode (DE-588)4312758-7 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Electronic book text Galois-Theorie (DE-588)4155901-0 s Topologische Methode (DE-588)4312758-7 s 1\p DE-604 https://doi.org/10.1007/978-3-642-38871-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027645069&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027645069&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chovanskij, Askolʹd G. 1947- Topological Galois theory solvability and unsolvability of equations in finite terms Topologische Methode (DE-588)4312758-7 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4312758-7 (DE-588)4155901-0 |
| title | Topological Galois theory solvability and unsolvability of equations in finite terms |
| title_auth | Topological Galois theory solvability and unsolvability of equations in finite terms |
| title_exact_search | Topological Galois theory solvability and unsolvability of equations in finite terms |
| title_full | Topological Galois theory solvability and unsolvability of equations in finite terms Askold Khovanskii |
| title_fullStr | Topological Galois theory solvability and unsolvability of equations in finite terms Askold Khovanskii |
| title_full_unstemmed | Topological Galois theory solvability and unsolvability of equations in finite terms Askold Khovanskii |
| title_short | Topological Galois theory |
| title_sort | topological galois theory solvability and unsolvability of equations in finite terms |
| title_sub | solvability and unsolvability of equations in finite terms |
| topic | Topologische Methode (DE-588)4312758-7 gnd Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Topologische Methode Galois-Theorie |
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| work_keys_str_mv | AT chovanskijaskolʹdg topologicalgaloistheorysolvabilityandunsolvabilityofequationsinfiniteterms |