Field Theory

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

About the first edition:

" ...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
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