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Silvester J.R. — Introduction to Algebraic K-Theory
Silvester J.R. — Introduction to Algebraic K-Theory

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Название: Introduction to Algebraic K-Theory

Автор: Silvester J.R.

Аннотация:

Algebraic K-theory is the name given to a body of theory which may be regarded in the first instance as an attempt to generalize parts of linear algebra, notably the theory of dimension of vector spaces, and determinants, to modules over arbitrary rings. The subject gets its name from its notation - given a ring R, one constructs groups called K0R, K1R, K2R, ... - and is called algebraic K-theory, rather than just K-theory, because it derives from (topological) K-theory, which is to do with the topology of vector bundles.
The intention of this text is to make algebraic K-theory accessible at a more elementary level than heretofore...


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 263

Добавлена в каталог: 15.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
${D}_{n}$-ring      136
${GE}_{n}$-ring, GE-ring      114
Algebra      45
Algebra, exterior      45
Algebra, tensor      45
Alternating map      44
Annihilator      39
Anticommutative tensor product      46
Artinian ring      26
Automorphism      3 92
Balanced map      13
Basis      5
Bilinear map      13
Bimodule      12
Cartesian square      154
Category      17 78 79
Category, directed      103
Category, fibre      141
Category, loop      78 95
Category, small      87
Category, with product      83
Category, with product and composition      93
Central extension      186
Chinese remainder theorem      22 68
Class group      64
Class number      65
Cofinal functor      143
Cofinal subcategory      91
Coherence      83
Comaximal ideals      68
Commutative diagram      5
composition      93
Congruence subgroup      181
Connected component      54
Connected ring      53
Constant rank      36
Covering space      229
D-ring, ${D}_{n}$-ring      132
Dedekind domain      66 77
Determinant      58 78 112 122 170
Diagonal element of ST(R)      210
Dieudonne determinant      124
Direct limit      104
Direct sum      3
Directed category      103
double      176
Dual module      36
Elementary linear group      109
Elementary matrix      99 109 183
Epimorphism      2
Epimorphism, split      6
EQUIVALENCE      83
Equivalent categories      83
Evaluation map      40
Extension, central      186
Exterior algebra      45
Exterior power      43
Fibre category      141
Field of fractions      31 61
Finitely generated module      7
First isomorphism theorem      3
Fractional ideal      61
Free module      5
Full subcategory      87
functor      17 78 80
Functor, cofinal      143
Functor, product-preserving      85
Fundamental group      115 229
General linear group      92 101
Graded algebra      45
Grothendieck group      8 16 78 87 93
Group of units      20
H-ideal      235
H-ring      232
Homomorphism      1 2
Ideal      18
Ideal, comaximal      68
Ideal, fractional      61
Ideal, H-      235
Ideal, invertible fractional      64
Ideal, radical      217
Ideal, trace      40
Idempotent      52
Idempotent, decomposition      55
Idempotent, lifting      53 243
Image      2
Invariant basis number      11 107 112
Invertible fractional ideal      64
Invertible module      41
Isomorphism      3 82
Isomorphism, stable      9
Isomorphism, theorem, first      3
Jacobson radical      25
Kernel      2
Local ring      22
localization      33 34
Loop construction      78 95
Matrix, elementary      99 109 183
Matrix, monomial      194
Matrix, permutation      194
Matrix, ring      23
Matsumoto's Theorem      207 227 248 249
Mayer — Vietoris sequence      160 162 170
Mennicke — Bass — Lazard — Serre, theorem      192 226
Module      1
Module, dual      36
Module, finitely generated      7
Module, free      5
Module, invertible      41
Module, of fractions      31
Module, projective      5
Module, quotient      2
Moebius band      89
Monomial element of ST(R)      210
Monomial matrix      194
Monomorphism      2
Morphism      79
Multilinear map      43
Nakayama's lemma      20
Natural equivalence      82
Natural transformation      82
Nil radical      52
Nilpotent element      52
Noetherian ring      54
Object      79
Orthogonal idempotents      55
Permutation matrix      194
Picard group      42 78
Prime spectrum      49
Principal fractional ideal      64
Product of rings      19
Product, category with      83
Product-preserving functor      85
Projective module      5
Quotient module      2
Radical, ideal      217
Radical, Jacobson      25
Radical, nil      52
Rank      29 35
Rank, constant      36
Rank, continuity of      50
Rank, map      51
Reduced Grothendieck group      28
refinement      55
Rehmann's theorem      248
Ring      1
Ring, ${D}_{n}-$      136
Ring, Artinian      26
Ring, connected      53
Ring, D, ${D}_{n}-$      132
Ring, GE-, ${GE}_{n}-$      114
Ring, H-      232
Ring, local      22
Ring, matrix      23
Ring, Noetherian      54
Ring, of fractions      30
Ring, semi-local      28 69 114 140 232 244 247
scalar      1
Schur's lemma      26
Section of a bundle      89
Semi-local ring      28 69 114 140 232 244 247
Simple module      26
Skeletal subcategory      87
Small category      87
Special linear group      113
Special orthogonal group      115
Special Whitehead group      113
Split epimorphism      6
Stable elementary linear group      111
Stable general linear group      108
Stable special linear group      113
Stably isomorphic modules      9
Steinberg group      184
Steinberg relations      184
Steinberg symbol      226
Subcategory      87
Subcategory, cofinal      91
Subcategory, full      87
Subcategory, skeletal      87
Submodule      2
Symbol      197 208 214
Symbol, Steinberg      226
Tensor algebra      45
Tensor power      43
Tensor product      12
Tensor product, of algebras      46
Tensor product, of homomorphisms      14
Topological K-theory      89
Trace ideal      40
Unimodular      116
UNITS      20 181
Vector bundle      89
Wedderburn — Artin theorem      27
Whitehead group      78 92 95 97 107
Whitehead lemma      111
Zariski topology      49
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