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Silvester J.R. — Introduction to Algebraic K-Theory
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Название: Introduction to Algebraic K-TheoryАвтор: 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.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1981Количество страниц: 263Добавлена в каталог: 15.05.2011Операции: Положить на полку |
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136 114 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, 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, 136 Ring, Artinian 26 Ring, connected 53 Ring, D, 132 Ring, GE-, 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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