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Hilton P.J., Stammbach U. — A course in homological algebra
Hilton P.J., Stammbach U. — A course in homological algebra



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Название: A course in homological algebra

Авторы: Hilton P.J., Stammbach U.

Аннотация:

This classic book provides a broad introduction to homological algebra, including a comprehensive set of exercises. Since publication of the first edition homological algebra has found a large number of applications in many different fields. Today, it is a truly indispensable tool in fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In this new edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. The background assumes little more than knowledge of the algebraic theories groups and of vector spaces over a field.


Язык: en

Рубрика: Математика/Алгебра/Гомология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 338

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Isomorphism      42
Isomorphism of modules      13
Isomorphism, modulo projectives      159
J-homology      324
J-objects over V      321
Jacobi identity      230
Kan extension      322 329
Kernel      13 17 50 61
kernel object      61
Killing form      244
Koszul complex      252
Koszul resolution      252
Kunneth formula      166
Ladder of an exact couple      269
Largest abelian quotient Qab      230
Law of composition      40
Left adjoint      64
Left adjoint, complete      292
Left adjoint, exact contravariant functor      135
Left adjoint, module      11
Levi — Malcev Theorem      250
Lie algebra      229
Lie algebra, abelian      230
Lie algebra, homomorphism      230
Lie bracket      229
Lie ideal      230
Lie subalgebra      230
LIMIT      72 276
Limit of a Rees system      288
Limit of a spectral sequence      259
Linearly independent      22
Long exact cohomology sequence      121
Long exact Ext-sequence      139 141
Long exact homology sequence      121
Long exact sequence of derived functors      136 137
Long exact Tor-sequence      161
Lower central series      204 239
Lyndon      201
Lyndon — Hochschild — Serre spectral sequence      303
Mac Lane      7 185
Magnus      206
Mapping cone      120
Maschke theorem      227
Mayer — Vietoris sequence      221
Module      11
Monomorphic      29 48
Monomorphism      29 48
Morphism      40
Morphism of bidegree(k, l)      75
Morphism of complexes      117 118
Morphism of degree k      75
Multiplicator      185
n-extension      148
Natural equivalence      51
Natural transformation      51
Nilpotent group      204
Nilpotent radical      251
Notational conventions for spectral sequences      264
Object      40
Object over X      60
Objectwise split      325
Opposite category      46
Periodic cohomology      200
Pext      312
Positive chain complex      126
Positive cochain complex      129
Positive double complex      298
Presentation , Projective      89
Presentation of a group      205
Presentation, $\mathscr{E}$-projective      308
Presentation, Finite      26 205
Presentation, Flat      115
Presentation, Injective      94
Principal crossed homomorphism      195
Principal ideal domain      26
PRODUCT      54
Product, preserving functor      58
Projection      20 54
Projective class of epimorphisms      308
Projective dimension      142
Projective module      23
Projective object      81
Projective rel $\varepsilon$      307
Projective resolution      127
Pull-back      60
Pure sequence      15
Push-out      62
Radical      250
Radical, Nilpotent      251
RANGE      41
Rank      107
Reduction Theorem      213 214
Rees system      283
Rees system, Special      283
Relative Ext      320
Relative homological algebra      306
Relative injective      211
Relative projective      211
Relative Tor      319
Relator      205
Representation of a group      13 227
Resolution      127 129
Resolution, $\mathscr{E}$-projective      308
Restriction      224
Reversing arrows      48
Right adjoint      64
Right adjoint, complete      292
Right adjoint, module      12
Satellite      313
schur      185 228
Section      206
Self-dual      50
Semi simple G-module      227
Semi simple Lie algebra      245
Semi-direct product of groups      195
Semi-direct product of Lie algebras      235
Short exact sequence      14 79
Skeleton of a category      54
Small category      52
Solvable Lie algebra      250
Spectral of a double complex      298
Spectral sequence      257
Spectral sequence functor      257
Spectral sequence, Bockstein      291
Spectral sequence, Grothendieck      299
Spectral sequence, Hochschild — Serre      305
Spectral sequence, Lyndon — Hochschild — Serre      303
Split extension of groups      196
Split of modules      85
Split short exact sequence      24
Splitting      24 196
Standard resolution      215 217
Stationary      265
Stein — Serre Theorem      106
Subcategory      43
Submodule      13
SUM      76
Surjective homomorphism      13
Tensor product      109
Tensor product of chain complexes      168
Terminal      43
Topological product      55
Tor      112 160
Torsionfree abelian group      107 115
Total degree      264
TRANSFER      228
Trivial $\mathfrak{g}$-module      232
Trivial G-module      187
Underlying functor      45 63
UNIT      65
Universal coefficient theorem      176 179
Universal enveloping algebra      230
Universal enveloping algebra, construction      54 59 70
Universal property      20 54
Weyl theorem      248
Whitehead lemmas      247
Yext      148
Yoneda      148
Yoneda, embedding      54
Yoneda, lemma      54
Yoneda, product      155
Zero morphism      43
Zero object      43
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