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| Jategaonkar A.V. — Localization in Noetherian Rings |
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| Предметный указатель |
 -homogeneous module 269
Affiliated series 121 239
Algebra, finite 16 296
Algebra, Lie 298
Algebra, Weyl 2 7
Annihilator 6
Annihilator, right ideal 6
AR property 81ff 140ff
AR ring 84 140ff 225
AR separated ring 224
Artin radical 131
Artinian quotient module 217
Artinian quotient ring 33 211ff
Assassinator 98
Assassinator prime ideal 98
Associated prime ideal 68
Bimodule 18
Bimodule, affiliated series of 121 239
Bimodule, Noetherian 120ff
Bimodulecellular series of 122
Bimoduleirreducible 2 48
Bimodules, subdirect product of 132
BOND 12 3ff
Bond, degenerate internal 140
Bond, density condition for 176
Bond, girth of 178
Bond, internal 139
Bonded rings 124
Bounded uniform dimension 167 199
cell 122
Cellular series 122
Centrally separated ring 225 263ff
Chain 2 86
Clan 2
Classical 193ff
Classical in comparability condition for 151 156 185 191 193 226 238 243
Classical, clique 193ff
Classical, localization 78 188
Classical, order 35
Classical, primary decomposition 243ff
Classical, semi-local ring 78
Classical, subset of spec R 187
Classically 78 83 188 203ff.
Classically, fully semi-primary ring 244
Classically, localizable semi-prime ideal 78 83 188 203
Classically, primary ideal 244
CLIQUE 136 140ff 171 172 193 227
Closed submodule, lo 39
Cogenerated torsion class 10 67
Common multiple 3
Common multiple property 3
Completely prime ideal 14 162 195 300
Compressible module 45ff 59 270
Condition, density 176 183
Condition, incomparability 151 156 185 191 193 226 238 243
Condition, intersection 190 191 194ff 200
Condition, Ore 3 7
Condition, second layer 187 188 202 219 226 251 285
Condition, strong second layer 220 226 251
Convention 39 59
Cotame simple module 280
Countable set xii
Critical module 2 70
CYCLE 2 86
Decomposition of injectives 92ff
Dedekind ring 289
Degenerate internal bond 140
Degenerate strongest link 181
Dense submodule 10 39
Density condition 176 183
Derivation 20 299
Deviation 2 33 2 34
Deviation of 233 2 34
Dimain 7
Dimain, Ore 7 37
Dimension, classical Krull 230 238
Dimension, GK 2 38
Dimension, global 134
Dimension, Krull 157 234ff 269ff
Dimension, semi-simple 24 41
Dimension, uniform 42 96
Directed graph (see Link graph)
Discrete poset 2 33
Enough clans 205
Enough invertibles 2 89
Equivalent, prime ideals 135 (see Clique)
Equivalent, prime rings 124ff
Essential subdirect sum 42 96
Essentially compatible 43
examples of 16ff.
Extension 16
Faithful ideal 306
FBN ring 162 171 199 236
FC-subgroup 306
finite 16
Finite, algebra 16 296
Finite, dimensional module 36
Finite, dimensional ring 36 37
Finite, extension 16
First layer 111 117 252
Fractional right ideal 2 76
Fully, bounded Noetherianring (see FBN ring)
Fully, classical ring 205 245
Fully, semi-primary ring 241ff 247
Fundmanetal, prime ideals 252 256ff 266
Fundmanetal, series 251 252 270ff
Generalized 17 61 122 212 249
Generalized matrix ring 17 61 122 212 249
Generic regularity (see Sparsity)
girth 178 183
GK dimension 2 38
Global dimension 134
Goldie ideal 66ff 71
Goldie ring 37
Goldie ring, semi-prime 57
Goldie's Theorem 32 5 7
Graph of a ring 136
Graph, directed (see Link graph)
Graph, locally finite 171
Group, orbitally sound 306
Group, p-nilpotent 309
Group, polycyclic 305
Group, polycyclic-by-finite 305
Group, ring 305ff
Heart of a ring 133
Hereditary ring 2 75
Hereditary subset of spec R 144
HNP ring 275ff
HNP ring with enough invertibles 289
Ideal, classically localizable semiprime 78 83 188 203ff
Ideal, classically primary 244
Ideal, completely prime 14 162 195 300
Ideal, faithful 306
Ideal, fractional 276
Ideal, Goldie 66ff 71
Ideal, Idempotent 14
Ideal, invertible 85 207 279 287ff.
Ideal, irreducible 242
Ideal, localizable semi-prime 71ff
Ideal, minimal prime 38 155 212ff
Ideal, polycentral 86 141 207
Ideal, polynormal 86 141 206ff
Ideal, primary 241 244
Ideal, prime radical of 69
Ideal, reflexive 210
Ideal, singular 56
Idealizer 29
Idempotent ideal 14
Incomparability condition 151 156 185 191 193 226 238 243
Incomparable prime ideals 105 156
| Indecomposable nodule 42
Injective module 15 92 290
Injective module,  layer of 252ff.
Injective module, bimodule 248
Injective module, decomposition of 92ff
Injective module, first layer of 111 117 252
Injective module, fundamental series of 251 270ff.
Injective module, ideal 242
Injective module, pleasant 284 287
Injective module, ring 2 42
Injective module, stem of 284 290ff.
Injective module, tame 115 151 251ff.
Injective module, unpleasant 284 287
Injective module, wild 115 151 251ff.
Internal bond 139
Intersection condition 190 191 194ff. 200
Intersection condition for 19
interval 2 33
Invertible ideal 85 207 279 287ff.
Jacobson radical 72
Jacobson's conjecture 79 120 246ff. 2 72
Krull dimension 157 234ff. 269ff.
Krull dimension, classical 230 238
Layer 116ff.
Layer, 252ff.
Layer, first 111 252
Layer, second (see Second layer)
Levitzki's theorem 62
Lie algebra 298
Link 119 135ff. 139ff. 145 151ff. 157 169 175 183
Link graph 136 140ff. 145 171
Link in comparability condition for 151 156 185 191 193 226 238 243
Link, girth of 183
Link, right 135
Link, second layer 135 154
Link, strongest 181ff. 184
Link, trivial 135 141 206 244
Local ring 72
Local!zability criterion 108 116 228
Localizable semi-prime ideal 71ff.
localization 2 71ff. 187
Localization at 12 88ff.
Localization at torsion class 12 88ff.
Localization atcogenerated 10 67
Localization atdefined 11 39 67
Localization atgenerated 11
Localization, classical 78 188
Localization, Ore 2 88
Localization, Partial 217 229
Localization, right 2 71ff. 187
Locally finite 159 167ff. 171 172 224
Locally finite, link graph 159 167ff. 171 172 224
Locally finite, subset of spec R 171
Main Lemma 151ff. 190 203 239 253
Matrix ring 16
Maximal order 210
Minimal prime ideal 38 155 212ff.
Module, -homogeneous 269
Module, annihilator of 6
Module, Artinian quotient 217
Module, assassinator of 98
Module, compressible 45ff. 59 2 70
Module, cotame simple 2 80
Module, critical 2 70
Module, finite dimensional 36
Module, first layer of 111 117 252
Module, fundamental primes of 252 256ff. 266
Module, fundamental series of 251 252 270
Module, indecomposable 42
Module, Jacobson radical of 72
Module, Krull dimension of 234ff. 269ff.
Module, localization of 8
Module, monoform 163 270
Module, nth layer of 252ff.
Module, P-tame 115
Module, P-torsionfree top of 165
Module, P-wild 115
Module, primary 100 105 183 257
Module, primary decomposition of 68 97 101 104 115 241
Module, p—primary 100 183 25 7
Module, quotient 8
Module, S-primary 105
Module, S-torsion 67
Module, S-torsionfree 67
Module, semi-simple 41
Module, semi-simple dimension of 41
Module, serial 285
Module, socle series of 77 271
Module, tame 115 151 251ff.
Module, torsion 10 39 59 67
Module, torsionfree 10 39 59 67
Module, torsionless 48ff.
Module, totally unfaithful 22 3
Module, uniform 42 104
Module, uniform dimension of 42 96
Module, uniserial 282
Module, wild 115 151 251ff.
Modules, essential subdirect sam of 42 96
Modules, similar 43 118
Modules, sub isomorphic 45
Modules, subdirect sum of 42
Mono form module 16 3 2 70
Multiplicative set 2
Multiplicity 112 118 175ff.
Nil radical 62 212ff.
Nil radical of 62 212ff.
Noetherian bimodule 120ff.
Normal element 84
Normalization 155
Normally separated ring 225
Nth layer 252ff.
Orbitally sound group 306
Order 33
Order in Artinian ring 33 211
Order in semi-simple ring 33 37 5 3
Order in skew field 33
Order, classical 35
Order, maximal 210
Order, right 33
Ore's Theorem 3 7
Ore, condition 3 7
Ore, domain 7 37
Ore, localization 2 88
Ore, set 3 11 146
P-nilpotent group 309
P-perfect extension 88
P-primary module 100 183 257
Partial localization 217 229
Period 285 268 296
Pleasant injective 284 287
Polycentral ideal 86 141 2 07
Polycentral ring 87ff. 226 300ff. 308
Polycyclic group 305
Polycyclic-by-finite group 305
Polynormal ideal 86 141 206ff.
Polynormal ring 87ff. 226 301 308
POSET 233
Primary, decomposition 68 97ff. 101 104 115 241 244
Primary, ideal 241 244
Primary, module 100 105 183 25 7
Primary, ring 241
Primary, submodule 101
Prime ideal xi
Prime ideal, assassinator 98
Prime ideal, associated 68
Prime ideal, completely 14 162 195 300
Prime ideal, fundamental 252 256ff. 266
Prime ideal, minimal 38 155 212ff.
Prime ideal, second layer condition for 188
Prime ideal, strong second layer condition for 220
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