Advanced Algebra

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Springer Science & Business Media, Nov 26, 2007 - Mathematics - 730 pages
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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

Key topics and features of Advanced Algebra:

*Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra

*Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry

*Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications

*Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis

*Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry

*Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems

*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics

Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra.

 

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Contents

VII
1
VIII
8
IX
12
X
24
XI
31
XII
35
XIII
38
XIV
50
LXI
342
LXII
349
LXIII
353
LXIV
368
LXV
371
LXVI
382
LXVII
388
LXVIII
397

XV
56
XVI
61
XVII
67
XVIII
76
XIX
77
XX
81
XXI
87
XXII
89
XXIII
94
XXIV
104
XXV
111
XXVI
114
XXVII
117
XXVIII
118
XXIX
120
XXX
123
XXXI
124
XXXII
132
XXXIII
135
XXXIV
145
XXXV
147
XXXVI
158
XXXVII
162
XXXVIII
166
XXXIX
167
XL
171
XLI
184
XLII
192
XLIII
202
XLIV
210
XLV
223
XLVI
232
XLVII
250
XLVIII
262
L
266
LI
274
LII
279
LIII
288
LIV
298
LV
304
LVI
307
LVII
313
LVIII
314
LIX
320
LX
331
LXIX
403
LXX
404
LXXI
408
LXXII
414
LXXIII
423
LXXIV
428
LXXV
434
LXXVI
445
LXXVII
447
LXXVIII
448
LXXIX
451
LXXX
456
LXXXI
466
LXXXII
473
LXXXIII
488
LXXXIV
491
LXXXV
499
LXXXVI
508
LXXXVII
510
LXXXVIII
516
LXXXIX
520
XC
531
XCI
534
XCII
540
XCIII
552
XCIV
554
XCV
558
XCVI
559
XCVII
563
XCVIII
570
XCIX
579
C
590
CI
595
CII
600
CIII
604
CIV
618
CV
626
CVI
633
CVII
635
CVIII
638
CIX
649
CX
713
CXI
717
CXII
721
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