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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Kaplansky I. - Fields and rings |
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| Предметный указатель |
Adjoint 142
Algebra 87
Algebra, algebraic 88
Algebraic, algebra 88
Algebraic, closure 74-6
Algebraic, element 3
Algebraic, extension 5
Annihilator 81 148
Augmentation ideal 119
Burnsidefs, problem 101-2
Burnsidefs, theorem 99
Centroid 148
Chain 132
Chain condition, ascending 132-4
Chain condition, descending 87 132-4 155 171
Chinese remainder theorem 108-9
Closed, field or group 12
Closed, subspace 140
Closure 140
Closure, algebraic 74-6
Closure, normal 29
Closure, split 29
Completely reducible 120
Composition series 133
Constructible number 8-9
Dedekind ring 171
Degree of element 5
Degree of field extension 2
Density theorem 95
DIMENSION 2
Dimension, global 171 191
Dimension, injective 186
Dimension, projective 168
Discriminant 50
Dual, full 139
Dual, vector spaces 139
Endomorphism 94
Enveloping ring 147
Enveloping ring, reduced 149
Equivalence, injective 186
Equivalence, projective 168
Ext 187
Extension, algebraic 5
Extension, infinite algebraic 74
Extension, radical 32 60-73
Extension, simple 48-9
Extension, transcendental 5
Field, algebraically closed 66
Field, finite 45-7
Field, ordered 66-8 73
Field, perfect 58
Field, splitting 23
Field, tower of 2
Functional 139
Galois, group 10
Galois, theory 16
Group, algebra 115 174
Group, locally finite 101
Group, torsion 101
Hilbertfs theorem 90 42
Hopkins 1
Hopkins, theorem 132-4
Ideal, maximal 83 91
Ideal, nil potent 88
Ideal, primitive 84
Ideal, radical 86
Ideal, regular 83-4
Ideal, topologically nil 89
| Identity, polynomial 156-161
Identity, standard 157 160
Injective, dimension 186
Injective, equivalence 186
Injective, module 185
Inner product 139
Kolchinfs theorem 100 136-7
Kuroschfs problem 102 160-1
Levitzkis theorem 135-6
localization 181
Locally finite, algebraic 102
Locally finite, group 101
Maximal, ideal 83 91
Maximal, subfield 154-6
Module 81
Module, completely reducible 120
Module, faithful 82
Module, injective 185
Module, irreducible 82
Module, projective 165 167
Module, unitary 81 133
Nilpotent, group 138
Nilpotent, ideal 88
Nilpotent, topologically 89
Norm 39
normal 12
Polynomial, identity 157
Polynomial, ring 174
Primitive with minimal ideal 139-146
Primitive, ideal 83
Primitive, ring 82
Projective, dimension 168
Projective, module 165 167
Purely inseparable 55
Quasi-regular 84-5
Radical of a ring 87 178
Radical, ideal 86
Radical, ring 85
Regular 110
Regular, ideal 83
Regular, local ring 183-5
Regular, representation 116
Regular, ring 110
Regular, semi-simple 87 171
Regular, simple 91 147 198
Related idempotents 127
Representation of algebra 121
Representation of group 121
Resolvent cubic 52
Ring, central simple 149
Ring, Dedekind 171
Ring, local 182
Ring, nil 8 5
Ring, polynomial 174
Ring, primitive 82 149
Ring, radical 85
Ring, regular local 183-5
Ruler and compass constructions 8-9
SBI 124
Schanuelfs lemma 167
Schurfs lemma 94
Separable 26 55
Stable 19
Tensor product 150
Trace 39 99
Transitive 51 52 95
Unipotent 100 136-8
Wedderburn principal theorem 124-130
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