Algebraic Patching

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields&...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Jarden, Moshe (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
Σειρά:Springer Monographs in Mathematics,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Jarden, Moshe.  |e author. 
245 1 0 |a Algebraic Patching  |h [electronic resource] /  |c by Moshe Jarden. 
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490 1 |a Springer Monographs in Mathematics,  |x 1439-7382 
505 0 |a 1. Algebraic Patching -- 2. Normed Rings -- 3. Several Variables -- 4. Constant Split Embedding Problems over Complete Fields -- 5. Ample Fields -- 6. Non-Ample Fields -- 7. Split Embedding Problems over Complete Fields -- 8. Split Embedding Problems over Ample Fields -- 9. The Absolute Galois Group of C(t) -- 10. Semi-Free Profinite Groups -- 11. Function Fields of One Variable over PAC Fields -- 12. Complete Noetherian Domains -- Open Problems -- References -- Glossary of Notation -- Index. 
520 |a Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$. 
650 0 |a Mathematics. 
650 0 |a Algebra. 
650 0 |a Field theory (Physics). 
650 0 |a Group theory. 
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650 2 4 |a Algebra. 
650 2 4 |a Field Theory and Polynomials. 
650 2 4 |a Group Theory and Generalizations. 
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776 0 8 |i Printed edition:  |z 9783642151279 
830 0 |a Springer Monographs in Mathematics,  |x 1439-7382 
856 4 0 |u http://dx.doi.org/10.1007/978-3-642-15128-6  |z Full Text via HEAL-Link 
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950 |a Mathematics and Statistics (Springer-11649)