000			03400nam a22004575i 4500
001			978-0-387-87575-0
003			DE-He213
005			20251006084427.0
007			cr nn 008mamaa
008			110406s2009 xxu| s |||| 0|eng d
020			_a9780387875750
020			_a99780387875750
024	7		_a10.1007/978-0-387-87575-0 _2doi
100	1		_aWeintraub, Steven H. _eauthor.
245	1	0	_aGalois Theory _h[electronic resource] / _cby Steven H. Weintraub.
264		1	_aNew York, NY : _bSpringer New York, _c2009.
300			_aXIV, 212p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_ato Galois Theory -- Field Theory and Galois Theory -- Development and Applications of Galois Theory -- Extensions of the Field of Rational Numbers -- Further Topics in Field Theory -- Transcendental Extensions.
520			_aThe book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions. Key topics and features of this second edition: - Approaches Galois theory from the linear algebra point of view, following Artin; - Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity. Review from the first edition: "The text offers the standard material of classical field theory and Galois theory, though in a remarkably original, unconventional and comprehensive manner ... . the book under review must be seen as a highly welcome and valuable complement to existing textbook literature ... . It comes with its own features and advantages ... it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable ... just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 (15), 2006) Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).
650		0	_aMATHEMATICS.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aGROUP THEORY.
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aGROUP THEORY AND GENERALIZATIONS.
650	2	4	_aNUMBER THEORY.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387875743
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-87575-0 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59319 _d59319