| 000 | 02656nam a22004815i 4500 | ||
|---|---|---|---|
| 001 | 978-3-642-15128-6 | ||
| 003 | DE-He213 | ||
| 005 | 20140220083746.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 110103s2011 gw | s |||| 0|eng d | ||
| 020 |
_a9783642151286 _9978-3-642-15128-6 |
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| 024 | 7 |
_a10.1007/978-3-642-15128-6 _2doi |
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| 050 | 4 | _aQA150-272 | |
| 072 | 7 |
_aPBF _2bicssc |
|
| 072 | 7 |
_aMAT002000 _2bisacsh |
|
| 082 | 0 | 4 |
_a512 _223 |
| 100 | 1 |
_aJarden, Moshe. _eauthor. |
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| 245 | 1 | 0 |
_aAlgebraic Patching _h[electronic resource] / _cby Moshe Jarden. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011. |
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| 300 |
_aXXIV, 292 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
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| 505 | 0 | _a1. 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 | _aAssuming 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 | _aMathematics. | |
| 650 | 0 | _aAlgebra. | |
| 650 | 0 | _aField theory (Physics). | |
| 650 | 0 | _aGroup theory. | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aAlgebra. |
| 650 | 2 | 4 | _aField Theory and Polynomials. |
| 650 | 2 | 4 | _aGroup Theory and Generalizations. |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783642151279 |
| 830 | 0 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
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| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-642-15128-6 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c107024 _d107024 |
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