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Bass H. — Algebraic K-theory
Bass H. — Algebraic K-theory



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Название: Algebraic K-theory

Автор: Bass H.

Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 762

Добавлена в каталог: 18.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E(M_1,\dots,M_n; q)$      182
$E_n(A,q)$      220
$GL_n(A,q)$      224
$G_i(A)\: (i=0,1)$      453
$H_S$      491—514
$K_1(A,q)$      229
$K_i(A)\: (i=0,1)$      447
$K_i(A)\: (i=0,1)$, exact sequence of      447—448
$M_S(A)$      491—514
$SK_1(A,q)$      229
$S^{-1}$      105
$\Sigma A$      344—353
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 of automorphisms      5
Category of diagrams      6
Category of endomorphisms      5
Category of modules      51—76
Category of morphisms      6
Category with product      344
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, quotient      417
Category, R-      57
Category, semi-simple      389
Category, sub-      2
Category, sub-, admissible      388
Category, sub-, Serre      417
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
Dedekind ring      137
Determinant, $\det\colon \mathrm{P} \to \mathrm{Pic}$      462—464
Determinant, $\det_i(A)\: (i=0,1)$      465
Devissage, reduction by      400—405
Dieudonne's theorem      269
Dimension of a CW complex      737—740
Dimension of a noetherian space      92—104
Dimension of a polynomial ring      101
Dimension, global      120
Dimension, homological      120
Dimension, Krull      100
Dimension, P-      37
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
Dual module      165—170
Elementary automorphism      182
Elementary matrix      192 220
Elementary subgroup      580—581
Elementary, 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 induction      575
Exponent of a group      573
Factorial ring      144
Filtration, $C_0$      401
Filtration, characteristic      401
Filtration, finite      23
Finite generation criteria      274—278
Finite generation criteria of $K_0$ and $G_0$      545 717—719
Finite generation criteria of $K_1$ and $G_1$      550 555
Finite generation criteria of $SL_n(A)$      337 549
Finite generation criteria of units      548 619—620 716
Five lemma      24
FP      514
FP, $K_i(FP), i=0$      515
FP, $K_i(FP), i=1$      519
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 $\pi$-graded algebra      199
Graded module      635—640
Graded object      39
Graded ring      635—640 643—652
Grothendieck group      346
Grothendieck theorem for $G_0(A[T])$      640
Grothendieck theorem for $K_0(A[T])$      636
Grothendieck theorem on reduction by resolution      407
H(A)      5 122
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 extension      113
Integral, closure      115
Integrally closed      115
Invertible ideal      127—148
Invertible module      132
Invertible submodule      134
Irreducible component      93
Jordan — Hoelder      23
Jordan — Hoelder series      24
Jordan — Hoelder theorem      24
Kernel      10
Krull ring      127—148
Krull — Schmidt theorem      20
Kubota's theorem      298 299—303
Lattice      93
Lattice, A-      155
Lattice, A-, right, left, two-sided      156
Lattice, R-      148
Lattice, R-, divisorial      150
LIMIT      7-12
Limit, inductive (or direct)      44 see
Local ring      87
localization      104-113
Localization, exact sequence of a      417—437 491—514
Localization, exact sequence of a, for Dedekind rings      702
M(A)      5
Mapping cone      30 741
Matrix      13
Matrix notation      13
Matrix permutation      227
Matrix, Cartan      453—458
Matrix, elementary      192—220
Max(A)      102
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, set of      1
Nakayama's lemma      85
Natural transformation      2
Nil(A)      652
Nine lemma      30
Noetherian      92
Noetherian lattice      94
Noetherian module      94
Noetherian ring      94
Noetherian space      97
Object, final      8
Object, graded      39
Object, initial      8
Object, projective      22 52
Object, simple      24
Object, zero      8
Opposite category      1
Order, maximal      154
Order, R- (in a semi-simple algebra)      152
P(A)      5
p-group      560
PGL      521
Picard $K_i(Pic)\: (i=0,1)$      460
Picard category, Pic      131
Picard group, Pic      71 132
Picard, $\det\colon\mathrm{Pic}\to\mathrm{P}$      460
Picard, Pic(A,q)      461
Picard, Pic(A,S)      136
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 module      69-71
Projective object      22
Projective, faithfully      52
Projective, over local rings      91
Projective, stable structure of      165—218
Pullback      9
Quasi-compact      97
Radical of a module      84
Radical, Jacobson      84
Rank $\mathrm{rk}\colon K_0 \to H_0$      459
Rank $\mathrm{Rk}_0(A)$      459
Rank of a projective module      130
Rank of unit groups      548—549
Rank, f-      167
Reciprocity laws in number fields      325—331
Reciprocity laws of Weil      333
Reciprocity laws on algebraic curves      331—342
Reciprocity laws, equivalence with Mennicke symbols      316
Reciprocity laws, functorial properties of      70
Reciprocity laws, power      328
Reciprocity laws, q-      314
Reduced norm      152 273 457
Reduced trace      152
Regular multiplicative set      125
Regular ring      122
Res(C)      32
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