000			03484nam a22005175i 4500
001			978-3-642-38841-5
003			DE-He213
005			20140220082913.0
007			cr nn 008mamaa
008			130911s2013 gw | s |||| 0|eng d
020			_a9783642388415 _9978-3-642-38841-5
024	7		_a10.1007/978-3-642-38841-5 _2doi
050		4	_aQA161.A-161.Z
050		4	_aQA161.P59
072		7	_aPBF _2bicssc
072		7	_aMAT002010 _2bisacsh
082	0	4	_a512.3 _223
100	1		_aKhovanskii, Askold. _eauthor.
245	1	0	_aGalois Theory, Coverings, and Riemann Surfaces _h[electronic resource] / _cby Askold Khovanskii.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
300			_aVIII, 81 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aChapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals -- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups -- 1.3 Field Automorphisms and Relations between Elements in a Field -- 1.4 Action of a k-Solvable Group and Representability by k-Radicals -- 1.5 Galois Equations -- 1.6 Automorphisms Connected with a Galois Equation -- 1.7 The Fundamental Theorem of Galois Theory -- 1.8 A Criterion for Solvability of Equations by Radicals -- 1.9 A Criterion for Solvability of Equations by k-Radicals -- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations -- 1.11 Finite Fields -- Chapter 2 Coverings: 2.1 Coverings over Topological Spaces -- 2.2 Completion of Finite Coverings over Punctured Riemann Surfaces -- Chapter 3 Ramified Coverings and Galois Theory:  3.1 Finite Ramified Coverings and Algebraic Extensions of Fields of Meromorphic Functions -- 3.2 Geometry of Galois Theory for Extensions of a Field of Meromorphic Functions -- References -- Index.
520			_aThe first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aGeometry, algebraic.
650		0	_aField theory (Physics).
650		0	_aGroup theory.
650		0	_aTopology.
650	1	4	_aMathematics.
650	2	4	_aField Theory and Polynomials.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aTopology.
650	2	4	_aAlgebra.
650	2	4	_aAlgebraic Geometry.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642388408
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-38841-5
912			_aZDB-2-SMA
999			_c98341 _d98341