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| Lang S. — Algebra |
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| Предметный указатель |
Exponential 497
Ext 791 808 810 831 857
Extension of base 623
Extension of derivations 375
Extension of fields 223
Extension of homomorphisms 347 378
Extension of modules 831
Exterior, algebra 733
Exterior, product 733
Extreme point 883
Factor, group 14
Factor, module 119 141
Factor, ring 89
Factorial 111 115 175 209
Faithful 28 334 649 664
Faithfully flat 638
Fermat theorem 195 319
Fiber product 61 81
Field 244
Field of definition of a representation 710
Filtered complex 817
Filtration 156 172 426 814 817
Finite, complex 762
Finite, dimension 141 772 823
Finite, extension 223
Finitely generated, algebra 121
Finitely generated, extension 226
Finitely generated, group 66
Finitely generated, module 129
Finitely generated, ring 90
Finitely presented 171
Fitting ideal 738—745
Fitting lemma 440
Five lemma 169
Fixed, field 261
Fixed, flat 612 808
Fixed, for a module 616
Fixed, point 28 34 80
Forgetful functor 62
Form, multilinear 450 466
Form, polynomial 384
Formal power series 205
Fourier coefficients 679
Fractional ideal 88
Fractions 107
Free resolution 840
Free resolution, homological dimension 772 823
Free resolution, module 129
Free resolution, resolution 763
Free resolution, sequence 877
Free resolution, set 877
Free resolution, type 129
Free resolution, under a place 349
Free, abelian group 38 39
Free, extension 362
Free, generators 137
Free, group 66 82
Free, module 135
Free, module generated by a set 137
Free, resolution 763
Frey polynomial 198
Frobenius, element 180 246 316 346
Frobenius, reciprocity 686 689
Functionals 142
functor 62
Fundamental group 63
G or (G,*)-module 664 779
G-homomorphism 779
G-object 55
G-regular 829
G-set 27 55
g.c.d. 111
Galois, cohomology 288 302
Galois, extension 261
Galois, group 252 262 269
Galois, theory 262
Gauss lemma 181 209 495
Gauss sum 277
Gelfand — Mazur theorem 471
Gelfand — Naimark theorem 406
Gelfond — Schneider 868
Generate and generators for a group 9 23 68
Generate and generators for a module 660
Generate and generators for a ring 90
Generate and generators for an ideal 87
Generating function or power series 211
Generators and relations 68
Generic, forms 390 392
Generic, hyperplane 374
Generic, pfaffian 589
Generic, point 383 408
Generic, polynomial 272 345
Ghost components 330
GL 19 521 543 546 547
GL2 300 317 537 715
Global sections 792
Goursat’s lemma 75
Graded, algebra 172 631
Graded, module 427 751 765
Graded, morphism 765 766
Graded, object 814
Graded, ring 631
Gram — Schmidt orthogonalization 579 599
Grassman algebra 733
Greatest common divisor 111
Grothendieck, algebra and ring 778—782
Grothendieck, group 40 139
Grothendieck, power series 218
Grothendieck, spectral sequence 819
Group 7
Group, algebra 104 121
Group, automorphism 10
Group, extensions 827
Group, homomorphism 10
Group, object 65
Group, ring 85 104 126
Hall conjecture 197
Harmonic polynomials 354 550
Hasse zeta function 255
Height 167
Herbrand quotient 79
Hermite — Lindemann 867
Hermitian, form 533 571 579
Hermitian, linear map 534
Hermitian, matrix 535
Hilbert theorem 90 288
Hilbert theorem on polynomial rings 185
Hilbert — Serre theorem 431
Hilbert — Zariski theorem 409
Hilbert, Nullstellensatz 380 551
Hilbert, polynomial 433
Hilbert, syzygy theorem 862
Homogeneous 410 427 631
Homogeneous, algebraic space 385
Homogeneous, ideal 385 436 733
Homogeneous, integral closure 409
Homogeneous, point 385
Homogeneous, polynomial 103 107 190 384 436
Homogeneous, quadratic map 575
Homology 445 767
Homology, isomorphism 767 836
Homomorphism of complex 445 765
Homomorphism of groups 10
Homomorphism of inverse systems 163
Homomorphism of modules 119 122
Homomorphism of monoid 10
Homomorphism of representations 125
Homomorphism of rings 88
Homomorphisms in categories 765
Homotopies of complexes 787
| Horrock’s theorem 847
Howe’s proof 258
Hyperbolic, enlargement 593
Hyperbolic, pair 586 590
Hyperbolic, plane 586 590
Hyperbolic, space 590
Hyperplane 542
Hyperplane, class group 88 126
Hyperplane, Ideal 86
Hyperplane, section 374 410
Idempotent 443
Image 11
Indecomposable 440
Independent, absolute values 465
Independent, characters 283 676
Independent, elements of module 151
Independent, extensions 362
Independent, variables 102 103
INDEX 12
Induced, character 686
Induced, homomorphism 16
Induced, module 688
Induced, ordering 879
Induced, representation 688
Inductively ordered 880
Inertia, form 393
Inertia, group 344
Infinite, cyclic group 8 23
Infinite, cyclic module 147
Infinite, extension 223 235
Infinite, Galois extensions 313
Infinite, period 8 23
Infinite, set 876
Infinite, under a place 349
Infinitely, large 450
Infinitely, small 450
Injective, map ix
Injective, module 782 830
Inner automorphism 26
Inseparable, degree 249
Inseparable, extension 247
Integers mod n 94
integral 334 351 352 409
Integral, closure 336 409
Integral, domain 91
Integral, equation 334
Integral, extension 340
Integral, homomorphism 337
Integral, map 357
Integral, root test 185
Integral, valued polynomials 216 435
Integrality criterion 352 409
Integrally closed 337
Invariant of linear map 557 560
Invariant of matrix 557
Invariant of module 153 557 563
Invariant of submodule 153 154
Invariant, bases 550
Invariant, submodule 665
Inverse ix 7
Inverse limit 50 51 161 163 169
Inverse limit of Galois groups 313 328
Inverse matrix 518
Invertible 84
Irreducible, algebraic set 382 408
Irreducible, character 669 696
Irreducible, element 111
Irreducible, module 554
Irreducible, polynomial 175 183
Irreducible, polynomial of a field element 224
Irrelevant prime 436
Isolated prime 422
Isometry 572
Isomorphism 10 54
Isomorphism of representations 56 667
Isotropy group 27
Iss’sa — Hironaka theorem 498
Jacobson, density 647
Jacobson, radical 658
Jordan canonical form 559
Jordan — Holder 22 156
K-family 771
K-theory 139 771—782
Kernel of bilinear map 48 144 522 572
Kernel of homomorphism 11 133
Kolchin’s theorem 661
Koszul complex 853
Krull — Remak — Schmidt 441
Krull, theorem 429
Krull, topology 329
Kummer extensions, abelian 294—296 332
Kummer extensions, non-abelian 297 304 326
L-functions 727
Lambda operation 217
Lambda-ring 218 780
Langlands conjectures 316 319
Lattice 662
Law of composition 3
Lazard’s theorem 639
Leading coefficient 100
Least, common multiple 113
Least, element 879
Least, upper bound 879
Left, coset 12
Left, derived functor 791
Left, exact 790
Left, ideal 86
Left, module 117
Length of complex 765
Length of filtration 433
Length of module 433 644
Lie above, prime 338
Lie above, valuation ring 350
Lie algebra 548
Lifting 227
Linear, combination 129
Linear, dependence 130
Linear, independence 129 150 283
Linear, map 119
Linear, polynomial 100
Linearly disjoint 360
Local, degree 477
Local, homomorphism 444
Local, norm 478
Local, parameter 487
Local, ring 110 425 441
Local, uniformization 498
localization 110
Locally nilpotent 418
Logarithm 497 597
Logarithmic derivative 214 375
Mackey’s theorems 694
MacLane’s criterion 364
Mapping cylinder 838
Maschke’s Theorem 666
Mason — Stothers theorem 194 220
Matrix 503
Matrix of bilinear map 528
Matrix, over non-commutative ring 641
Maximal, abelian extension 269
Maximal, archimedean 450
Maximal, element 879
Maximal, ideal 92
Metric linear map 573
Minimal polynomial 556 572
Mittag — Leffler condition 164
Modular forms 318 319
Module 413
Module, over principal ring 146 521
Modulo an ideal 90
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