000			03372nam a22004935i 4500
001			978-0-387-27678-6
003			DE-He213
005			20161121231023.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387276786 _9978-0-387-27678-6
024	7		_a10.1007/0-387-27678-5 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aRoman, Steven. _eauthor.
245	1	0	_aField Theory _h[electronic resource] / _cby Steven Roman.
250			_aSecond Edition.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXII, 335 p. 18 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v158
505	0		_aPreliminaries -- Preliminaries -- Field Extensions -- Polynomials -- Field Extensions -- Embeddings and Separability -- Algebraic Independence -- Galois Theory -- Galois Theory I: An Historical Perspective -- Galois Theory II: The Theory -- Galois Theory III: The Galois Group of a Polynomial -- A Field Extension as a Vector Space -- Finite Fields I: Basic Properties -- Finite Fields II: Additional Properties -- The Roots of Unity -- Cyclic Extensions -- Solvable Extensions -- The Theory of Binomials -- Binomials -- Families of Binomials.
520			_aThis book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity. For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities. From the reviews of the first edition: The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study. - T. Albu, Mathematical Reviews ...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study. - J.N.Mordeson, Zentralblatt.
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	_aNumber Theory.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387276779
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v158
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-27678-5
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507400 _d507400