Hilton P.J., Stammbach U. — A course in homological algebra :: Электронная библиотека попечительского совета мехмата МГУ

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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.

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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

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Предметный указатель

$(m, n)^{th}$ -Rung      274
$Q^{\varrhoup}$ -process      269
$Q_{\sigma}$ -process      270
$\mathfrak{g}$ -module      232
$\mathscr{E}$ -acyclic      320
$\mathscr{E}$ -acyclic complex      308
$\mathscr{E}$ -admissible morphism      308
$\mathscr{E}$ -derived functor      309
$\mathscr{E}$ -exact      308
$\mathscr{E}$ -projective      307
$\mathscr{E}$ -projective complex      308
$\mathscr{E}$ -satellite      313
Abelian category      74 78
Abelianized      45
Acyclic carrier      129
Acyclic carrier, (co)chain complex      126 129
AD      232
Additive category      75
Additive functor      78
Adjoint functor      64
Adjoint theorem      318
Adjugant equivalence      64
Adjunction      65
Algebra graded      172
Algebra, associative      112
Algebra, augmented      112
Algebra, exterior      239
Algebra, Internally graded      172 251
Algebra, tensor      230
Associated bilinear form      244
Associated bilinear form, graded object      262
Associative law      41
Associativity of product      56
Augmentation ideal of $\mathfrak{g}$       232
Augmentation ideal of G      187 194
Augmentation of $U_{\mathfrak{g}}$       232
Augmentation of $\mathbb{Z}G$       187
Balanced bifunctor      96 146 161
Bar resolution      214 216 217
Basis of a module      22
Bicartesian square      271
Bifunctor      47
Bigraded module      75
Bilinear function      112
Bimodule      18
Birkhoff — Witt Theorem      74 231
Bockstein spectral sequence      291
Boundary      118
Boundary, operator      117
Buchsbaum      317
Cartan, H.      186
Cartesian product of categories      44
Cartesian product of sets      55
Category      40
Category of abelian groups $\mathfrak{U}\mathfrak{b}$       42
Category of functors      52
Category of groups $\mathfrak{G}$       42
Category of left $\Lambda$ -modules $\mathfrak{M}^l_A$       43
Category of models      329
Category of right $\Lambda$ -modules $\mathfrak{M}^r_A$       43
Category of sets $\mathfrak{G}$       42
Category of topological spaces $\mathfrak{I}$       42
Category with zero object      43
Center of a group      228
Center of a Lie algebra      233
Central extensions      209
Chain      118
Chain complex      117
Chain complex of homomorphisms      169
Chain complex, acyclic      126
Chain complex, Filtered      263
Chain complex, First total      167
Chain complex, Flat      172
Chain complex, Positive      126
Chain complex, projective      126
Chain complex, Second total      167
Chain map      117
Chain map of degree n      177
Change of rings      163 190 318
Characteristic class      210
Closed class of epimorphisms      307
Coboundary      118
Coboundary operator      118
Cochain      118
Cochain complex      118
Cochain complex, Acyclic      129
Cochain complex, Injective      129
Cochain complex, Positive      129
Cochain map      118
Cocycle      118
Codomain      41
Coequalizer      50
Cofiltering category      326
Cofiltration      264 292
Cofinal functor      323 326
Cofree module      33 35
Cogroup      59
Cohomological dimension      223
Cohomologous      118
Cohomology class      118
Cohomology functor      118
Cohomology module      118
Cohomology of a coproduct      219
Cohomology of a group      188
Cohomology of a Lie algebra      234
Cohomology ring of a group      219
Coinduced      211
Coinitial      43
Cokernel      13 17 50
Colimit      276
Commutative diagram      14
Commutative K-algebras      329
Commutativity of product      56
Comparison theorem      268
Complementary degree      264
Completely reducible representation      227
Completing a filtration      294
Composition of morphisms      40
Conjugation      225
Connected category      71
Connected sequence of functors      312
Connecting homomorphism      99 121 136 137
Constant functor      69 276
Contavariant functor      46
Contracting homotopy      125
Coproduct      58
Corestriction      225
Counit      65
Covariant functor      46
Crossed homomorphism      194
Cup-product      219
CYCLE      118
Cyclic groups, (co)homology of      200
Deficiency      205
Degenerate      215
Derivation of a group      194
Derivation of a Lie algebra      234
Derivation, f-      196
Derived couple      258
Derived functor      130 134
Derived length      250
Derived series      249
Derived system of a Rees system      284
Diagonal action      212
Diagonal functor      69 276
Diagonal homomorphism      212
diff      329
Differential      117 118
Differential module with involution      172
Differential object      256

Dimension, Cohomological      223
Dimension, global      147 251
Dimension, injective      147
Dimension, projective      142
Direct factor      36
Direct limit      72 280
Direct product      20
Direct sum      18 19
Direct summand      24
Discrete category      72
Divisible module      31
Domain (of a morphism)      41
Double complex      167 169
Dual      29
Duality      46 48
Dualization      28
Eckmann      5 185
Eilenberg      185
Eilenberg — Zilber theorem      166
Embedding of a subcategory      45
Enough injectives      129
Enough projectives      128
Epimorphic      29 48
Epimorphism      29 48
Equalizer      50
Equivalent categories      51
Equivalent extensions of groups      206
Equivalent extensions of Lie algebras      238
Equivalent extensions of modules      84
Essential extension      36
Essential monomorphism      36
Exact coproducts      326
Exact couple      257
Exact functor, Left      134
Exact functor, Right      132
Exact on projectives      137
Exact sequence      14 80
Exact sequence, 5-term      202
Exact square      80
Ext      89 94 139 143
Extension of groups      206
Extension of Lie algebras      238
Extension of modules      84
Exterior power      239
Factor set      210
Faithful functor      47
Faithful representation of a Lie algebra      245
Fibre map      147
Fibre product      62
Filtered chain complex      263 281
Filtered differential object      261
Filtered object      262
Filtration of a double complex, First      297
Filtration of a double complex, Second      297
Filtration, Complete      292
Filtration, finite      267
Filtration, Homologically finite      267
Finite convergence      265 267
Finitely presentable group      205
Five lemma      15
Flat module      111
Free functor      45 63
Free Lie algebra      236
Free module (on the set S)      22
Free object in a category      81
Free product of groups      58
Free product with amalgamated subgroup      62 221
Freudenthal      185
Full embedding      47
Full embedding theorem      74
Full functor      47
Full subcategory      43
functor      44
Functor category      52
Functor represented by A      46
G-acyclic object      299
G-module      186
Generator of a category      44
Generator of a group      205
Generator of a module      22
Global dimension      147 251
Graded algebra      172
Graded algebra, Differential      172
Graded algebra, Internally      172 251
Graded module      75
Graded module, Internally      251
Graded object, Associated      262
Graded, Negatively      266
Graded, Positively      266
Grothendieck group      72 74
Grothendieck spectral sequence      299
Group algebra over K      12 165
Group in a category      58
Group of homomorphisms      16
Group presentation      205
Group representation      13 227
Group ring      186
Group ring over $\Lambda$       188
Gruenberg resolution      218
Hilton      5
Hochschild — Serre spectral sequence      305
Hom-Ext-sequence      100 102
Homologous      118
Homology class      118
Homology functor      118
Homology module      118
Homology module of a complex      118
Homology module of a coproduct      219
Homology module of a functor      324
Homology module of a group      188
Homology module of a Lie algebra      237
Homology module of a product      221
Homology module of a small category      327
Homology module of an augmented algebra      330
Homology module of cyclic groups      200
Homomorphic relation      290
Homomorphism of modules      13
Homotopic      124
Homotopic morphisms of double complexes      305
Homotopy      124
Homotopy category      126
Homotopy class      43
Homotopy equivalence      126
Homotopy type      126
Homotopy, Contracting      125
Hopf      185
Hopf algebra      212
Hopf's formula      204
Hurewicz      185
Identity functor      45
Identity functor, morphism      41
Image      13 75
Induced module      210
Inflation      224
Initial      43
Injection      19 58
Injective class of monomorphisms      308
Injective dimension      147
Injective envelope      38
Injective homomorphism      13
Injective module      30 36
Injective object      81
Injective resolution      129
Invariant element      191 234
Inverse homomorphism      13
Inverse homomorphism, limit      72
Invertible functor      45
Invertible functor, morphism      42
Isomorphic      42
Isomorphic category      45

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