03401nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003100137050001400168072001600182072002300198082001200221100002800233245006000261250002000321264004600341300004400387336002600431337002600457338003600483347002400519490005300543505054800596520130601144650001702450650001302467650002802480650001902508650001702527650001302544650003402557650001902591710003402610773002002644776003602664830005302700856004402753912001402797999001902811952007702830978-0-387-27678-6DE-He21320180115171354.0cr nn 008mamaa100301s2006 xxu| s |||| 0|eng d a97803872767869978-0-387-27678-67 a10.1007/0-387-27678-52doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aRoman, Steven.eauthor.10aField Theoryh[electronic resource] /cby Steven Roman. aSecond Edition. 1aNew York, NY :bSpringer New York,c2006. aXII, 335 p. 18 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aGraduate Texts in Mathematics,x0072-5285 ;v1580 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. 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. 0aMathematics. 0aAlgebra. 0aField theory (Physics). 0aNumber theory.14aMathematics.24aAlgebra.24aField Theory and Polynomials.24aNumber Theory.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387276779 0aGraduate Texts in Mathematics,x0072-5285 ;v15840uhttp://dx.doi.org/10.1007/0-387-27678-5 aZDB-2-SMA c369337d369337 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK