000 03752nam a22005295i 4500
001 978-0-387-27678-6
003 DE-He213
005 20181204131308.0
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
040 _aISI Library, Kolkata
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aRoman, Steven.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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 _aAlgebra.
650 0 _aField theory (Physics).
650 0 _aNumber theory.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387508429
776 0 8 _iPrinted edition:
_z9781441920959
776 0 8 _iPrinted edition:
_z9780387276779
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v158
856 4 0 _uhttps://doi.org/10.1007/0-387-27678-5
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425084
_d425084