# Field Theory

Springer Science & Business Media, Nov 17, 2005 - Mathematics - 335 pages

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials – the Kummer theory.

This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included.

" ...the author has gotten across many important ideas and results. 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

"The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study."

- T. Albu, MathSciNet

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### Contents

 III 1 IV 2 V 10 VII 14 VIII 16 X 17 XII 21 XIII 23
 LXI 173 LXII 174 LXIII 179 LXIV 180 LXV 182 LXVI 197 LXVII 208 LXVIII 211

 XIV 24 XV 27 XVI 32 XVIII 33 XIX 35 XX 41 XXII 42 XXIII 46 XXIV 47 XXV 53 XXVI 54 XXVII 56 XXVIII 58 XXIX 63 XXX 66 XXXI 73 XXXII 75 XXXIII 77 XXXIV 84 XXXV 85 XXXVI 88 XXXVII 91 XXXVIII 93 XXXIX 96 XL 100 XLI 105 XLII 108 XLIII 111 XLIV 113 XLV 114 XLVI 116 XLVII 117 XLVIII 119 XLIX 121 L 124 LI 128 LII 130 LIII 135 LIV 137 LV 143 LVI 148 LVII 154 LVIII 159 LIX 164 LX 165
 LXIX 212 LXX 213 LXXI 214 LXXII 215 LXXIV 218 LXXV 219 LXXVI 223 LXXVII 225 LXXVIII 232 LXXIX 234 LXXX 236 LXXXI 238 LXXXII 239 LXXXIII 241 LXXXIV 250 LXXXV 251 LXXXVI 253 LXXXVII 257 LXXXVIII 261 LXXXIX 266 XC 269 XCI 270 XCII 273 XCIII 274 XCIV 276 XCV 278 XCVI 280 XCVII 282 XCVIII 287 XCIX 289 C 296 CI 304 CII 307 CIII 309 CIV 310 CV 312 CVI 316 CVII 319 CVIII 320 CIX 324 CX 325 CXI 327 CXII 329 Copyright