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Авторизация |
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Поиск по указателям |
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Bass H. — Algebraic K-theory |
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Предметный указатель |
182
220
224
453
229
() 447
(), exact sequence of 447—448
102
-group 560
229
105
344—353
514
, (), 515
, (), 519
491—514
5 122
5
491—514
(and ) 652
5
32
Affine group 186
Algebra, augmented 197
Algebra, exterior 462
Algebra, group 158
Algebra, monoid 158 159
Algebra, separable 153
Algebra, symmetric 521—528
Artin — Lam cyclic exponent theorem 586
Artinian lattice 93
Artinian module 94
Artinian ring 79 95
Augmented algebra 197
Bimodule 57
Bott’s theorem 747
Cancellation theorem 184
Cartan condition 533
Cartan homomorphisms 453
Cartan matrix 456
Cartesian product 2
Cartesian square 359
Cartesian, co 10
Category 1—7
Category, abelian 20
Category, abelian, K-theory in 387—444
Category, additive 12
Category, center of a 56
Category, directed 47
Category, fibre product 358—362
Category, k 437—444
Category, of automorphisms 5
Category, of diagrams 6
Category, of endomorphisms 5
Category, of modules 51—76
Category, of morphisms 6
Category, quotient 417
Category, R 57
Category, semi-simple 389
Category, sub 2
Category, sub-, admissible 388
Category, sub-, Serre 417
Category, with product 344
Center of a category 56
Center of a ring 56
Characteristic, Euler 406
Characteristic, polynomial 631
Characteristic, sequence of an endomorphism 630
Chinese remainder theorem (CRT) 92
Class number (finiteness of) 544
Closed point 102
Codimension 98
Cofinal functor 345
Cofinal functor, exact sequence of a 369—382
Cofinal pair 360
Cohn’s theorem 202
Coimage 10
Cokernel 10
Colimit 10
Complete (J-adically) 88
COMPLEX 28
Complex, acyclic 29
Complex, bounded 28
Complex, contractible 29
Complex, CW 737—740
Complex, homotopic 29
Complex, Koszul 525
Complex, positive 28
Conductor of an abelian group ring 605—619
Coproduct 9 (see also Direct sum)
Dvissage, reduction by 400—405
Dedekind ring 137
Determinant, 462—464
Determinant, () 465
Dieudonn$\s theorem 269
Dimension, - 37
Dimension, global 120
Dimension, homological 120
Dimension, Krull 100
Dimension, of a CW complex 737—740
Dimension, of a noetherian space 92—104
Dimension, of a polynomial ring 101
Direct limit see Colimit
Direct sum 14
Dirichlet theorem 548
Discrete valuation ring (DVR) 137
Divisor 141
Divisor, group 140
Divisorial ideal 141
Divisorial lattice 148—164
Dual category 1-module 165—170
Elementary automorphism 182
Elementary matrix 192 220
Elementary subgroup 580—581
Elementary subgroup, hyper 580—581
Embedding theorem 22
EQUIVALENCE 4 60
Equivalence, criterion for 4
Equivalence, data 62
Equivalence, data, auto 71
Equivalence, data, pre 61
Euclidean algorithm 196
Euclidean ring 196
Euclidean ring, generalized 193
Exact functor 20—28
Exact sequence 21
Exact sequence, of a cofinal exact functor 391—400
Exact sequence, of a cofinal functor 369—382
Exact sequence, of a localization 491—514
Exact sequence, of a quotient functor 417—437
Exact sequence, of a triple 378—382
Exact sequence, short 21
Excision 382—386
Exponent of a group 573
Exponent, induction 575
Factorial ring 144
Filtration, - 01
Filtration, characteristic 401
Filtration, finite 23
Finite generation, criteria 274—278
Finite generation, of and 545 717—719
Finite generation, of and 550 555
Finite generation, of 337 549
Finite generation, of units 548 619—620 716
Five lemma 24
Fractional ideal 141
Free algebra 198
Free ideal ring (fir) 190
Free monoid 199
Free product of algebras 198
| Free product of groups 198—199
Frobenius functor 569
Frobenius G-module 570
Frobenius reciprocity 563
Full ring of fractions 134
functor 2
Functor, additive 18
Functor, adjoint 40
Functor, categories of 3
Functor, cofinal 46
Functor, constant 6
Functor, contracted 659
Functor, contravariant 2
Functor, E-surjective 356
Functor, exact 21
Functor, faithful 2 51
Functor, full 2
Functor, morphism of 2
Functor, product preserving 344
Functor, representable 7
Functor, right continuous 58
Fundamental theorem 663
Generator 52
Gersten’s theorem 699
Graded -graded algebra 199
Graded module 635—640
Graded object 39
Graded ring 635—640 643—652
Graded theorem, for 640
Graded theorem, for 636
Graded theorem, on reduction by resolution 407
Grothendieck group 346
Height (of a prime ideal) 100
Heller’s theorem 423
Hereditary ring 121
Hilbert basis theorem 96
Hilbert symbol 325—331
Hilbert syzygy theorem 632
Homology 29
Idempotents 87—89 103
Idempotents, lifting 88
Idempotents, orthogonal 88
Image 10
Indecomposable 19
Induction 562
Induction, principle 574
Induction, theorems (classical) 580—589
Integers 113
Integral closure 115
Integral extension 113
Integrally closed 115
Invertible ideal 127—148
Invertible module 132
Invertible submodule 134
Irreducible component 93
Jordan — Hlder 23
Jordan — Hlder series 24
Jordan — Hlder theorem 24
Kernel 10
Krull ring 127—148
Krull — Schmidt theorem 20
Kubota’s theorem 298 299—303
Lattice 93
Lattice, - 155
Lattice, -, right, left, two sided 156
Lattice, - 148
Lattice, -, divisorial 150
LIMIT 7—12
Limit, inductive (or direct) 44 (see also Colimit)
Local ring 87
localization 104—113
Localization, exact sequence of a 417—437 491—514
Localization, exact sequence of a, for Dedekind rings 702
Mapping cone 30 741
Matrix 13
Matrix,Cartan 453—458
Matrix,elementary 192—220
Matrix,notation 13
Matrix,permutation 227
Mayer — Vietoris pair 674
Mayer — Vietoris sequence 362—369
Mayer — Vietoris sequence, long 676
Mennicke symbols 282
Mennicke theorem 293
Milnor’s theorems 478—482
Module, categories of 51—76
Module, invertible 132
Module, projective see Projective modules
Module, S-torsion 125
Module, torsion (free) 156
Mordell — Weil theorem 717
Morphism of categories 3
Morphism of functors 2
Morphism, iso-, set of 1
Nakayama’s Lemma 85
Natural transformation 2
Nine lemma 30
Noetherian 92
Noetherian, lattice 94
Noetherian, module 94
Noetherian, ring 94
Noetherian, space 97
Object, 0 8
Object, final 8
Object, graded 39
Object, initial 8
Object, projective 22 52
Object, simple 24
Opposite category 1
Order, - (in a semi-simple algebra) 152
Order, maximal 154
PGL 521
Picard category, 131
Picard group, 71 132
Picard, () 460
Picard, 136
Picard, 461
Picard, det: 460
Product, cartesian 9
Product, category with 344—353
Product, co 10
Product, fibre 9 478—491
Product, free 190—209 697—700
Product, semi-direct 188
Projective faithfully 52
Projective module 69—71
Projective module, over local rings 91
Projective module, stable structure of 165—218
Projective object 22
Pullback 9
Quasi-compact 97
Radical, Jacobson 84
Radical, of a module 84
Rank, - 167
Rank, 459
Rank, of a projective module 130
Rank, of unit groups 548—549
Rank, rk: 459
Reciprocity laws, - 314
Reciprocity laws, equivalence with Mennicke symbols 316
Reciprocity laws, functorial properties of 709
Reciprocity laws, in number fields 325—331
Reciprocity laws, of Weil 333
Reciprocity laws, on algebraic curves 331—342
Reciprocity laws, power 328
Reduced norm 152 273 457
Reduced trace 152
Regular multiplicative set 125
Regular ring 122
Resolution 32
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