000			03437nam a22004695i 4500
001			978-0-387-31608-6
003			DE-He213
005			20250710083948.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387316086 _a99780387316086
024	7		_a10.1007/0-387-31608-6 _2doi
082	0	4	_a512 _223
100	1		_aLorenz, Falko. _eauthor.
245	1	0	_aAlgebra _h[recurso electrónico] : _bFields and Galois Theory / _cby Falko Lorenz.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aVIII, 296 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aConstructibility with Ruler and Compass -- Algebraic Extensions -- Simple Extensions -- Fundamentals of Divisibility -- Prime Factorization in Polynomial Rings. Gauss's Theorem -- Polynomial Splitting Fields -- Separable Extensions -- Galois Extensions -- Finite Fields, Cyclic Groups and Roots of Unity -- Group Actions -- Applications of Galois Theory to Cyclotomic Fields -- Further Steps into Galois Theory -- Norm and Trace -- Binomial Equations -- Solvability of Equations -- Integral Ring Extensions with Applications to Galois Theory -- The Transcendence of ? -- Fundamentals of Transcendental Field Extensions -- Hilbert's Nullstellensatz.
520			_aThe present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantine dimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews
650		0	_aMATHEMATICS.
650		0	_aALGEBRA.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aALGEBRA.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aCOMMUTATIVE RINGS AND ALGEBRAS.
650	2	4	_aNUMBER THEORY.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387289304
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-31608-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57147 _d57147