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| van den Essen A. — Polynomial automorphisms and the Jacobian conjecture |
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| Предметный указатель |
(Algebra) membership algorithm 289
(Krull) dimension 276
Abhyan kar-Sathaye Conjecture 86 99 103 105
Abhyankar 13 67 75 85 86 93 99 100 103 105 106 115 116 239 251—254 257 272 286
Abhyankar — Moh theorem 12 93 106 115 116
Abhyankar — Moh — Suzuki theorem 85 99
Abhyankar's reduction theorem 251—254 257 272
Action,  -action 35 206 219—223 227—229
Additive group 2(34 229 277
Adjamagbo 11 70 74—76 83 84 239 244 257 261
Adjoint operator 298
Affine parametric line 271
Affine subgroup 47
Affine variety 203 217 218 220 226 271 278 285 296 305
Alev 49 60 95 239 271 273
Algebraic group action 203 205 215 220
Algebraic set 77 79 80 99 119 271 283—285
Algorithm 37 42 63 65—68 75 85 289
Algorithm, (algebra) membership algorithm 289
Algorithm, Derksen's algorithm 203 211 214
Algorithm, elimination algorithm 65 288
Algorithm, extendibility algorithm 37 67 68
Algorithm, ideal membership algorithm 288
Algorithm, image membership algorithm 37 39 42 68 226
Algorithm, invertibility algorithm 61 63
Algorithm, kernel-algorithm 37 38 42 203 220 222 236 237
Algorithm, normal form algorithm 287
Algorithm, Reconstruction algorithm 67 75
Algorithm, relation algorithm 39 288
Amalganmted free product 85—89 94 95 115 116 216
Analytic linearizable 136
Anick 49 60 97
Anick's example 49 60
Appelgate 255
Associated graded ring 21
Attractor 176 177 179 181—185 189 196 303
Attractor, global attractor 176 179 181—183 185 188 196
Attractor, local attractor 176
Automorphism theorem 86 99 100
Baba 255
Basin of attraction 176 201
Bass 41 42 60 117 125 141 222 226 263 273 292
Beauville 225
Bemat 175
Bernstein 296
Bernstein inequality 296
Berson 20 21 237
Bhatwadekar 237
Birational cancellation problem 225
Birational isomorphism 284 285
Campbell 60 240 242
Cancellation problem 54 203 215 217—219 225 237
Chamarie 49 60
Characteristic variety 296
Chau 43 125 127 175 215
Cheng 169 270
Choudary 86 99 103 116 237
Cima 170 175 179 182 185 189 191 201 239 242
Classification problem 31
Clearing map 3 8 9 58 121
CLLC 195—198
CM-ring 280
Coefficient-topology 242
Cohen — Macaulay ring 280
Cohn 255
Colliot-Thelene 225
Commutator 95 295
Commutator subgroup 95
Complementary Conjecture 104
Completely reducible 206
Completion 15 257 279 292
Conjecture, Abhyankar — Sathaye Conjecture 86 99 103 105
Conjecture, CLLC 195—198
Conjecture, Complementary Conjecture 164
Conjecture, Dixmier Conjecture 264
Conjecture, DMZ-Conjecture 186 195 196
Conjecture, Exponential Generators Conjecture 42 47
Conjecture, Fixed point conjecture 179 180 182
Conjecture, JacobJan Conjecture 6 13 15 42 43 48 52—55 57 60 82 97 99 104 117 120 125 127 129 131 145 169 175 178—180 185 187 195 239 241 242 2.5 251 253—257 260—265 270 273 292
Conjecture, kambayashi's Linearization Conjecture 215
Conjecture, Markus — Yamabe Conjecture 175 177 180 185 190—192
Conjecture, Real Jacobian Conjecture 239 241 242
Conjecture, Samuelson Conjecture 240
Conjecture, Sathaye Conjecture 103—105
Conjecture, Stable tameness conjecture 118
Conjecture, Weak Dixmier Conjecture 264 273
Conjecture, Weak Jacobian Conjecture 256
Conjecture, Weak Markus — Yamabe Conjecture 177
Constants 18 21 116 129 164 177 180 181 183 220
Coordinate 5 52 70 92 102 177 182 200 208 215 223
Coordinate ring 278 283—285 300
Coordinate system 5 70
Coordinate, coordinate system 5 70
Coordinate, linear coordinate 10 56 100 101 126 143 165 199 239 270
Cormell 8 41 42 60 117 125 141 260 273
Cubic homogeneous polynomial map 59 75 125 131 145 186
Cubic linear polynomial map 117 125 131 195 196
Cylindrical variety 222
Cynk 80 84
Daigle 20 30 35 206 223 234 237 304
Danielewski 219
Dedekind ring 42 146 280
Degree 55 91 111 145 284 289
Degree, geometric degree 124 261 284 300
Degree, w-degree 91 93 245 251
Deng 185—189
Dependence problem 143 145 168 169
Depth 277 280
Derivation, elementary derivation 226 234
Derivation, inner derivation 20
Derivation, Jacobian derivation 30
Derivation, kernel of a derivation 3 18
Derivation, locally finite derivation 22 24 25
Derivation, locally nilpotent derivation 3 22 24—32 35 37 42—44 47—49 54 63 68 89 94 116 143 155 158 159 164 203 217 220—227 237 302 304
Derivation, locally nilpotent k-derivation 28 35 37 226
Derivation, nice derivation 143 158 164
Derivation, triangular derivation 20 26 32 34 36 118 119 164 225
Derivation, Winkelmann derivation 158
Derksen 11 19 42 60 85 95 116 159 164 187 203 211 214 218 237 257 270 302
Derksen's algorithm 203 211
Deveney 42 206 225 228 229 237
Dicks 89 115
Dillen 183 201
Dimca 86 99 103 116 237
DIMENSION 19 20 75 77 83 85 95 98 101 117 134 143 145 146 159 170 175 180 185 193 195—197 203 206 215 218 222 223 230 234 237 242 270—272
Dimension, (Krull) dimension 277
Direct image 265 298
Direction 245—247 249 251 252 263
Discrete Markus — Yamabe problem 179 190 191
Divergence 32 237
Dixmier 264 273
DMZ-Conjecture 186 187 189 190 195 196
Dominant map 284
Drensky 76
Druzkowski 42 59 75 117 125 131 136 140 141 168 169 190 195 237 239 272 305
Druzkowski map 125 131 136 169
Dutta 237
EDO 104 228
Eggermont 237
Elementarily equivalent 120
Elementary derivation 226 234
Elementary polynomial map 244
Elimination algorithm 65 213 288
Elliptic curve 35
Embedding 6 7 11 85 86 99—104 116—119 267 284 305
Embedding, exotic embedding 100 104
Embedding, standard embedding 100 102
Equivalent, elementarily equivalent 120
Equivalent, stably equivalent 120 121 124 143
Equivalent, tamely equivalent 120 126 130
| Exotic algebraic structure 116 218 219
Exotic embedding 100 104
Exponential automorphism 43 44 48
Exponential Generators Conjecture 42 47
Exponential map 16 159
Extendibility algorithm 37 67 68
Face polynomial 61 66 67 69 73 75 300
Factorially closed 28 34
Faithfully fiat 12 291 294 306
Fessler 175 178
Fiat homomorphism 291
Fiat map 293 294 305
Fiat module 291
Filtered ring 21
Finite representation 208 210
Finston 42 206 225 228 229 237
Fixed point conjecture 179 180 182
Fixed point free 223 225 226
Fixed point problem 217
Fixed point set 216 220—223 225
Flatness 42 291 292 294
Formal inverse function theorem 3 4 11 13 58 259 294
Formanek 13 42
Forstneric 116
Fournier 175 178
Freudenburg 20 206 223 234 237 304
Fujita 203 218 225 237
Furter 49 57 59 60 116 168 169 171
Gabber 60
Gabriel 42
Gale 240
Galois descent 9
Ganong 116
Gasull 170 175 179 182 185 191 201 239 242
Gehrke 237
Geometric degree 124
Global attractor 176 179 181—183 185 188 189 196
Globevnik 116
Glutsuk 178
Gomi 117 131 136 139 169 187 189 196
Gomi — Zampieri pairing 131 169 189 196
Gordan 206 211
Groebner basis 39 40 61 63—65 67 69 75 211 213 214 287—289
Group action 175 203 205 219 220
Group ring 23 36
Group, additive group 204 229 277
Group, affine subgroup 47 85
Group, algebraic group action 203 205 215 220
Group, commutator subgroup 95
Group, group action 175 203 205 206 215—217 219
Group, linear group 204
Group, multiplicative group 204
Group, nilpotency subgroup 43 47
Group, orthogonal group 204 215
Group, reductive group 203 206 209—211 215 216
Group, special linear group 204
Group, tame subgroup 85
Group, Torus group 204
Gutierrez 75 175 178
Gutwirth 115
Gwozdziewicz 256 272
hadamard 239 240
Hadas 116
Hartman 177
Height 22 74 277
hessian 183
Hilben 18 19 22 203 206 208 209 211 228 229 234 237
Hilbert 14-th problem 3 6 18 19 22 31 32 37 40 203 206 228 229 237 279 280 281 299
Hilbert 14-th problem, problem 18
Hilbert fourteen 228 234
Holonomic 263 265 269 273 296—298
Holonomic module 298
Hubbets 98 143—145 150 160 162 165 168 170 171 175 185 186 189 190 191 201 242
Ideal membership algorithm 288
Image membership algorithm 37 39 42 68 226
Inner derivation 20
Integral closure 17 30 54 146 279 280
Integral extension 29 106 279
Invarianl functions 205
Invenibility algorithm 61 63
Invenibility Problem 239
Inverse image 272 298
Inversion formula 61 73 75
Invertibility criterion 61 62 145
Invertible polynomial map xiii 5
Ivanenko 201
Jacobian derivation 30 31
Jacobian pair 239 245—247 249
JacobJan 239 241 242 251 253—257 263 265 270 292
JacobJan Condition 43 49 50 170 239
JacobJan mate 55 245 247 253 254 272
JacobJan polynomial 245 247 251 253 273
Jacobson radical 277
Jaeobian Conjecture 6 15 42 43 48 52—55 57 60 67 82 97 99 104 117 120 125 127 129 131 145 169 175 178—180 185 187 195 239 242 251 253—257 260—265 270 273 292
Jelonek 86 99 102 104 271—273
Joni 75
Jordan decomposition 22—25
Jung 85 86 89 115
Jung — van der Kulk theorem 85 89 115
Kaliman 102 105 116 218 237 256 273
Kambayashi 115 116 203 215
Kambayashi's Linearization Conjecture 215
Kang 84 116
Keller 6 11 12 42 54 129 130 141 145 185 254 255 256 264—266 269 270 294
Keller map 11 42 129 130 141 145 254—256 264—266 269 294
Keller's theorem 12 42 54 270
Kernel of a derivation 3 18
Kernel-algorithm 37 38 42 220 236
Kojima 237
Koms 218
Kraft 201
Krasovski 177
Kulikov 180
Kurdyka 240
Kutzschebauch 116
Kwiecifiski 75
Lang 141
LaSalle 175 179—182 185 189 190 192 196 200
LaSalle problem 179—182 185 192 196 200
Lefschetz-principle 3 6 7 30 56
Li 66 67 75
Libgober 70
Lie algebra 14 20
Linear coordinate 10 56 100 101 126 165 199 239 270 305
Linear group 204
Linear representation 206
Linearly triangulable 170
Llibre 175 242
Local attractor 176
Local ring 95 98 279 280 283 292
Locally asymptotically stable 176 177
Locally finite derivation 22 24 25
Locally nilpotent derivation 3 22 24—32 35 37 42—44 47—49 54 63 68 89 94 116 143 155 158 159 164 203 217 220—227 237 302 304
Locally nilpotent k-derivation 28 35 37
Lyapunov 175—177
Mafiosas 170 179 182 185 191 201 239 242
Magnus 254 255 272
Makar-Limanov 31 89 115 116 218 262
Map, clearing map 3 8 9 41 58 121
Map, cubic homogeneous polynomial map 59 75 125 131 143 145 148 186
Map, dominant map 284 285
Map, Druzkowski map 125 131 136 140 169
Map, elementary polynomial map 244
Map, exponential map 16 159
Map, flat map 293
Map, Keller map 11 42 129 130 141 145 254—256 264—266 269 294
Map, Nagata map 74 75 293
Map, negative polynomial map 125 127
Map, polynomial map 119 125 134 148
Map, positive polynomial map 127 130
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