An Introduction to Homological Algebra

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Cambridge University Press, Oct 27, 1995 - Mathematics - 450 pages
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The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras is also described. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors.
 

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Contents

II
1
III
5
IV
10
V
15
VI
18
VII
25
VIII
30
IX
33
XLVI
198
XLVII
203
XLVIII
206
XLIX
216
LI
219
LII
223
LIII
238
LIV
242

X
38
XI
43
XII
49
XIII
51
XIV
58
XV
66
XVII
68
XVIII
73
XIX
76
XX
80
XXI
87
XXII
91
XXIII
95
XXIV
99
XXV
104
XXVI
111
XXVII
115
XXVIII
120
XXIX
122
XXX
127
XXXI
131
XXXII
135
XXXIII
141
XXXIV
145
XXXV
150
XXXVI
153
XXXVII
160
XXXIX
167
XL
171
XLI
174
XLII
177
XLIII
182
XLIV
189
XLV
195
LV
248
LVI
254
LIX
259
LX
270
LXI
275
LXII
286
LXIII
294
LXIV
300
LXVI
311
LXVII
319
LXVIII
326
LXIX
330
LXX
338
LXXI
344
LXXII
354
LXXIII
362
LXXIV
369
LXXVII
373
LXXVIII
379
LXXIX
385
LXXX
390
LXXXI
394
LXXXII
398
LXXXIII
402
LXXXIV
407
LXXXV
417
LXXXVI
421
LXXXVII
423
LXXXVIII
424
LXXXIX
427
XC
429
XCI
432
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