| 000 | 03610nam a22005655i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-66182-2 | ||
| 003 | DE-He213 | ||
| 005 | 20251030113249.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 241029s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031661822 _9978-3-031-66182-2 |
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| 024 | 7 |
_a10.1007/978-3-031-66182-2 _2doi |
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| 050 | 4 | _aQA247-247.45 | |
| 050 | 4 | _aQA161.P59 | |
| 072 | 7 |
_aPBF _2bicssc |
|
| 072 | 7 |
_aMAT002010 _2bisacsh |
|
| 072 | 7 |
_aPBF _2thema |
|
| 100 | 1 |
_aHernandez, David. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _986769 |
|
| 245 | 1 | 0 |
_aIntroduction to Galois Theory _h[electronic resource] / _cby David Hernandez, Yves Laszlo. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2024. |
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| 300 |
_aXVII, 193 p. 47 illus., 11 illus. in color. _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 Undergraduate Mathematics Series, _x2197-4144 |
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| 505 | 0 | _a1 Invitation to Galois Theory -- 2 Basic Concepts of Group Theory -- 3 Basic Concepts of Ring Theory -- 4 Basic Concepts of Algebras Over a Field -- 5 Finite Fields, Perfect Fields -- 6 The Galois Correspondence -- 7 Addendum: Infinite Galois Correspondence -- 8 Cyclotomy and Constructibility -- 9 Solvability by Radicals -- 10 Reduction Modulo p -- 11 Complements -- 12 Review Exercises -- 13 Solutions to Exercises. | |
| 520 | _aThis textbook provides an undergraduate introduction to Galois theory and its most notable applications. Galois theory was born in the 19th century to study polynomial equations. Both powerful and elegant, this theory was at the origin of a substantial part of modern algebra and has since undergone considerable development. It remains an extremely active research subject and has found numerous applications beyond pure mathematics. In this book, the authors introduce Galois theory from a contemporary point of view. In particular, modern methods such as reduction modulo prime numbers and finite fields are introduced and put to use. Beyond the usual applications of ruler and compass constructions and solvability by radicals, the book also includes topics such as the transcendence of e and π, the inverse Galois problem, and infinite Galois theory. Based on courses of the authors at the École Polytechnique, the book is aimed at students with a standard undergraduate background in (mostly linear) algebra. It includes a collection of exam questions in the form of review exercises, with detailed solutions. | ||
| 650 | 0 |
_aAlgebraic fields. _970148 |
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| 650 | 0 |
_aPolynomials. _964269 |
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| 650 | 0 |
_aGroup theory. _970149 |
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| 650 | 0 | _aNumber theory. | |
| 650 | 1 | 4 |
_aField Theory and Polynomials. _970153 |
| 650 | 2 | 4 |
_aGroup Theory and Generalizations. _970154 |
| 650 | 2 | 4 | _aNumber Theory. |
| 700 | 1 |
_aLaszlo, Yves. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _986770 |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031661815 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031661839 |
| 830 | 0 |
_aSpringer Undergraduate Mathematics Series, _x2197-4144 _975368 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-66182-2 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 999 |
_c64570 _d64570 |
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