Algebra: Volume II: Fields with Structure, Algebras and Advanced Topics

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Springer Science & Business Media, Nov 24, 2007 - Mathematics - 340 pages

From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume II the reader can find: the theory of ordered fields (e.g., with reformulation of the fundamental theorem of algebra in terms of ordered fields, with Sylvester's theorem on the number of real roots), Nullstellen-theorems (e.g., with Artin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentals of the theory of quadratic forms, of valuations, local fields and modules. The book also contains some lesser known or nontraditional results; for instance, Tsen's results on solubility of systems of polynomial equations with a sufficiently large number of indeterminates. These two volumes constitute a very good, readable and comprehensive survey of classical algebra and present a valuable contribution to the literature on this subject.

 

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Contents

I
1
III
4
IV
5
V
7
VI
8
VII
10
VIII
11
IX
12
LXVI
128
LXVII
133
LXVIII
139
LXIX
142
LXX
143
LXXI
144
LXXII
148
LXXIII
149

X
15
XIII
16
XIV
18
XV
23
XVI
25
XVII
28
XIX
30
XX
32
XXI
34
XXII
37
XXIII
39
XXV
40
XXVI
45
XXVII
47
XXVIII
52
XXIX
54
XXX
56
XXXI
59
XXXII
65
XXXIV
67
XXXV
68
XXXVI
70
XXXVII
73
XXXVIII
75
XL
76
XLI
78
XLII
80
XLIII
81
XLIV
83
XLV
91
XLVI
92
XLVIII
94
XLIX
96
L
98
LI
100
LII
105
LIII
109
LV
110
LVI
112
LVII
114
LVIII
116
LIX
118
LX
121
LXI
122
LXII
123
LXIII
124
LXIV
127
LXXIV
151
LXXVI
152
LXXVII
155
LXXVIII
160
LXXIX
164
LXXX
166
LXXXI
168
LXXXII
173
LXXXIII
176
LXXXIV
182
LXXXVI
184
LXXXVII
190
LXXXVIII
194
LXXXIX
196
XC
203
XCI
212
XCII
217
XCIII
223
XCV
224
XCVI
226
XCVII
229
XCVIII
231
XCIX
234
C
239
CII
240
CIII
242
CIV
243
CV
247
CVI
249
CVII
251
CVIII
253
CX
254
CXI
259
CXII
261
CXIII
265
CXIV
268
CXV
272
CXVI
275
CXVII
277
CXVIII
282
CXX
284
CXXI
286
CXXII
288
CXXIII
294
CXXIV
299
CXXV
331
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About the author (2007)

Prof. Dr. Falko Lorenz lehrt an der UniversitAt MA1/4nster Mathematik und ist auswArtiges Mitglied der Akademie gemeinnA1/4tziger Wissenschaften zu Erfurt.

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