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| Jensen C.U., Lenzing H. — Model Theoretic Algebra with particular emphasis on Fields, Rings, Modules |
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| Предметный указатель |
Elementary equivalence, for separably closed fields 17
Elementary equivalence, for sets 99
Elementary equivalence, for torsion modules 109
Elementary equivalence, for weak global dimension 258—260
Elementary equivalence, localization of 114
Elementary equivalence, to algebraic number field 29
Elementary equivalence, to number field 66
Elementary equivalence, to polynomial ring 67 69 74
Elementary equivalence, to pure-injective envelope 158
Elementary equivalence, to Q[X] 36
Elementary extension 3
Elementary subfield 18
Elementary submodule 123 229 237 240 244
Elementary subring 3 74
Elimination of quantifiers 306
Elimination of quantifiers, for algebraically closed fields 307
Elimination of quantifiers, for modules 91—92
Ellentuck, E 172
Elliptic curve 70
Embedding dimension 265
Envelope, injective 128
Envelope, projective 187
Envelope, pure-injective 128
Epimorphism in category of rings 213 301
Ersov, Yu. L. 17
Essential map 272
Essential submodule 402
Essential supremum 233—234
Exact sequence 402
Exact sequence of functors 385
Exact sequence pure-exact 96 98
Existentially closed subfield 19
F-semiperfect ring 127 180 247—249 252 403
Factorial domain 50 75 318 402
Factorial ring 72
Faith, C. 163 183 281 247
Faithful functor 380
Faithful module 402
Field extension pure transcendental 75
Field,  23 41 43
Field, admissible 77
Field, algebraically closed 5 17 30—31 43 49 58—59 306 309
Field, Archimedean 41 48
Field, cubically closed 55
Field, finite 30—31 58 69
Field, formally real 21 25 28
Field, Henselian 31
Field, Hilbertian 75—76
Field, non-Archimedean 41 48 64
Field, of characteristic p 16—17
Field, of characteristic zero 16
Field, ordered 8—9
Field, Peano field 61
Field, Pythagorean 34—35 47
Field, quasi-algebraically closed 19
Field, real closed 9 21—23 26—28 30—31 41 43 45—49 58—59
Field, relatively algebraically closed 4
Field, rigid 63
Field, S-closed 87
Field, separably closed 17
Field, universally admissible 77—80 87 89
Filter 1
Filter,  -complete 140 152
Finite axiomatizability, for (m, n) -presented modules 228
Finite axiomatizability, for fields of characteristic p 16
Finite axiomatizability, for finite global dimension 263
Finite axiomatizability, for finite representation type 341
Finite axiomatizability, for G -admissible fields 77
Finite axiomatizability, for global dimension 346
Finite axiomatizability, for injective modules 123 245
Finite axiomatizability, for self-injective dimension 346
Finite field 30—31 58 69
Finite n-presentation 264
Finite simple group 78
Finitely axiomatizable class 15
Finitely definable subfunctor 135
Finitely definable subgroup 92—93 96—99 126 161 164 170—171 181
Finitely definable subgroup, of flat module 96—97
Finitely definable subgroup, of fp-injective module 98—99
Finitely generated free module 227
Finitely generated module 227
Finitely generated modules, elementary equivalence of 115
Finitely presented 93
Finitely presented module 93—94 96—98 107—108 112 228 234 368
Finitistic global dimension 235
Finitistic global dimension, conjectures 263 373
Finitistic projective dimension of ultraproduct 264
First order language of modules one-sorted 91
First order language two-sided 225
First order sentence 2
Fischbacher, U. 340
Fisher, J. W. 268
Fixman, U. 207—208
Flat dimension 369
Flat module 96—97 106 109 115—119 122—123 229—232 234—235 244 368
Flat module, rank of 244
Flat resolution 312
Formally real field 20—21 25—26 28
Formula, atomic 307
Formula, positive primitive 92 96 99—100 114
Formula, positive quantifier-free 307
Forster, O. 254
Fp-injective dimension 240 264 377
Fp-injective dimension of ultraproduct 240
Fp-injective functor 197
Fp-injective module 98—99 108 119 153 239 245 577
Free algebra 266 275 300
Free Boolean algebra 261 291
Free module 367
Free module of infinite rank 232—233 235—236
Freyd, P. 381
Fried, M. 77
Fuchs, L. 139 205
Full embedding of categories 380
Full functor 380
Full subcategory 380
Fuller, K. 234 247
Function field 28 30
Function field, Pythagoras number of 27
Function, semicontinuous 313
Functor, -injective 142—144 150—151
Functor, additive 379
Functor, dense 380
Functor, faithful 380
Functor, full 380
Functor, injective 126 131 143 145
Functor, preserving algebraic compactness 211 221
Functor, preserving elementary equivalence 211 221
Functor, representable 386
Functor, representative 380
Functor, uniform 199
Gabriel's theorem 313 343
Gabriel, P. 169 176 198 278 313 331 341 343 353 379
Gaifman, H. 63
Galois extension 77
Galois group 77
Galois group, abelian 85
Galois group, alternating 81
Galois group, cyclic of order four 82
Galois group, cyclic of prime power order 81
Galois group, dihedral 81—82 87
Galois group, finite 81
Galois group, of length t 84
Galois group, quaternion 81—82
Galois group, simple 80—81 87
Galois group, solvable 81 84
Galois group, symmetric 81 87
Garavaglia, S. 93 100 163 171
Geigle, W. 198 209 218 299 356
Gelfand, I. M. 169 207
| Gelfand-Kirillov dimension 275 277—278
Generalized Continuum Hypothesis 12 23 260
Generator in additive category 382 403
Geyer, W.-D. 6
Gillman, L. 24
Global dimension 254 278 332 339
Global dimension, finitistic 235 369
Global dimension, of ultrapower 260—261
Gobel, R. 63 139
Goblot, R. 152
Goedel's completeness theorem 309
Goldie dimension 238
Goodearl, K. 183
Gordon, R. 198 278 353
Goto, S. 254
Graded module 300
Grothendieck category 383
Group, affine algebraic 312
Group, finite simple 78
Group, S-semisimple 82—83
Group-graded module 300
Growth of algebra 275
Gruson, L. 92—93 125 127 131 155 163—164 292
Happel, D. 331
Harada, M. 165
Hartshorne, R. 310—311 313
Hasse principle 29
Hensel's lemma 145
Henselian field 31
Henselian ring 50—58 60 69 403
Hereditary Noetherian ring 232
Hereditary ring 214 254 403
Herrmann, C. 292 325 341
Herstein, I. N. 247 262
Hilbert's  problem 8—9 26
Hilbert's irreducibility theorem 75
Hilbert's Nullstellensatz 7 310
Hilbert, D. 75
Hilbertian field 75—76
Hochster, M. 352
Huppert, B. 82—83
Idempotent element 404
Immediate extension of valued fields 288
Indentity standard 273
Infinite descent 35 51
Injective dimension 3 123—124 240 369
Injective module 119—123 368
Injective object in abelian category 382
Injective resolution 368
Injectivity Baer's test for 368
Integrally closed ring 306 404
Irreducible map 335
J0ndnip, S. 183 220 256—257
Jacobson radical 243
Jacobson radical, of module 404
Jacobson radical, of polynomial ring 262
Jacobson radical, of power series ring 270
Jacobson radical, of ring 404
Jacobson semi-simple ring 247
Jacobson, N. 17 21 247
Jaffard, P. 249
Jarden, M. 77
Jensen, C. U. 18 92—93 123 125 127 131 155 163—164 172 192 194—195 260—261 263 292—293 299 325 341 348 355—356
Jerison, M. 24
Jonah, D. 244
Kaplansky's theorem, on pi-algebras 276
Kaplansky's theorem, on projective modules 235
Kaplansky, I. 8 169 183 205 235 260 288—289 291 295 356
Kasch, F. 247
Kato, K. 28
Keisler, H. J. 1 11—12 24 31 46 57 69 329
Keisler-Shelah's ultrapower theorem 3—4 11 16 32 91 112—113 212 231
Kielpinski, R. 155
Klein, R. 75
Klingen, N. 227
Kochen, S. 31 57
Kraft, H. 312—313
Krause, G. 275 378
Kreisel, G. 306
Krivine, J. L. 306
Kronecker algebra 193 404
Kronecker module 193 207—208 404
Kronecker module, p-adic 208
Kronecker module, preinjective 208
Kronecker module, preprojective 194
Kronecker module, regular 208 209
Kronecker, L. 207
Krull dimension 39 43—45 50 57 65 67 69 75 117—118 121 123 192 254 271 276—278 313
Krull dimension, classical 276 278
Krull dimension, for categories 198
Krull dimension, for mod(Ј) 198 200
Krull dimension, infinite 66 69
Krull dimension, of Peano ring 64
Krull dimension, sense of Gabriel 278
Krull dimension, sense of Gabriel-Rentschler 278
Krull filtration 198
Krull, W. 288
Krull-Schmidt theorem 324 332
Kulikov 291
Kumar, R. 254
Kunen, K. 329
Lagrange's theorem 24 27 63
Lambek, J. 127 249
Lang, S. 19 21 30 75
Language of modules one-sorted 91
Lattice 318—319
Lattice, projective 320
Lawrence, J. W. 268
Lazard, D. 229—230 234
Leap, D. 31
Left perfect ring 251
Lenagan, T. H. 275 378
Lenzing, H. 18 126 192 194—195 209 232 254 260 263 281 292—293 297 299 325 341 348 356
Level of field 21 25
Levitzki's theorem 165
Lifting of idempotents 248—249
Liiroth's theorem 70
Linearly compact module 174 289
Liouville numbers 49
Local dimension 313
Local module 238 241
Local ring 111 118 306 378 404
localization 112 114 116
Localization of elementary equivalence 114
Localization principle for flat modules 116
Localizing subcategory 198
Locally closed set 311
Locally coherent module 237
Locally finite module 244
Los's principle 2—3 5—6 8 11 15—16 21 27 227
Lowenheim-Skolem's theorem 4—6 24 164 235 237 261
M-adic module 205
Mac Lane separable 4 17—18 328
Machover 61
Map irreducible 335
Mapping diagonal 125
Martin's Axiom 172
Matlis, E. 121 283
Matzat, B. H. 77
Maximally complete, valuation ring 288 323
Maximally complete, valued field 288
Maximum condition, for open subschemes 315
Maximum condition, on n-generated submodules 244
Mazzola, G. 331
Michler, G. 183
Mitchell, B. 379 381 384 387
Mittag-Leffler, G. 293
Module,  -algebraically compact 160—161 163—164 169—171 193—195 216
Module, -algebraically compact indecom-posable 245
Module, -injective 122 239 245
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