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| Lang S. — Algebra |
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| Предметный указатель |
abc conjecture 195
Abelian 4
Abelian, category 133
Abelian, extension 266 278
Abelian, group 4 42 79
Abelian, Kummer theory 293
Abelian, tower 18
Absolute value 465
Absolutely semisimple 659
Abstract nonsense 759
Abut 815
Action of a group 25
Acyclic 795
Adams operations 726 782
Additive category 133
Additive functor 625 790
Additive polynomial 308
Adic, completion 163 206
Adic, expansion 190
Adic, topology 162 206
Adjoint 533 581
Adjoint functor 629
Affine space 383
Algebra 121 629 749
Algebraic, closure 178 231 272
Algebraic, element 223
Algebraic, extension 224
Algebraic, group 549
Algebraic, integer 371
Algebraic, set 379
Algebraic, space 383 386
Algebraically, closed 272
Algebraically, independent 102 308 356
Almost all 5
Alternating, algebra 733
Alternating, form 511 526 530 571 598
Alternating, group 31 32 722
Alternating, matrix 530 587
Alternating, multilinear map 511 731
Alternating, product 733 780
Annihilator 417
Anti-dual 532
Anti-linear 562
Anti-module 532
Approximation theorem 467
Aramata’s theorem 701
Archimedean ordering 450
Artin — Rees theorem 429
Artin — Schreier theorem 290
Artin, conjectures 256 301
Artin, theorems 264 283 290 429
Artinian 439 443 661
Associated, graded ring 428 430
Associated, group and field 301
Associated, ideal of algebraic set 381
Associated, linear map 507
Associated, matrix of bilinear map 528
Associated, object 814
Associated, prime 418
Associative 3
Asymptotic Fermat 196
Automorphism 10 54
Automorphism of a form 525 533
Automorphism, inner 26
Balanced 660
Banach space 475
Base change 625
Basis 135 140
Bateman — Horn Conjecture 323
Belong, group and field 263
Belong, ideal and algebraic set 381
Belong, prime and primary ideal 421
Bernoulli, numbers 218
Bernoulli, polynomials 219
Bifunctor 806
Bijective ix
Bilinear form 146 522
Bilinear map 48 121 144
Binomial polynomial 434
Blichfeldt theorem 702
BLOCKS 555
Borel subgroup 537
Boundaries 767
Bounded complex 762
Bourbaki theorems on sets 881
Bourbaki theorems on traces and semisimplicity 650
Bracket product 121
Brauer’s theorems 701 709
Bruhat decomposition 539
Burnside theorems on simple modules 648
Burnside theorems on tensor representations 726
Burnside theorems, butterfly lemma 20 6
Burnside theorems, dimension 772
Cancellation law 40
Canonical map 14 16
cardinal number 885
Cartan subgroup 712
Casimir 628 639
Category 53
Cauchy, family 52
Cauchy, sequence 51 162 206 469
Cayley — Hamilton theorem 561
Center of a group 26 29
Center of a ring 84
Central element 714
centralizer 14
Chain condition 407
CHARACTER 282 327 667 668
Character, independence 283 676
Characteristic 90
Characteristic polynomial 256 434 561
Characteristic polynomial of tensor product 569
Chevalley’s theorem 214
Chinese remainder theorem 94
Class formula 29
Class function 673
Class number 674
Clifford algebra 749 757
Closed, complex 765
Closed, subgroup 329
Closed, under law of composition 6
Coboundary 302
Cocycle, GL 549
Cocycle, Hilbert’s theorem 90 288
Cocycle, Sah’s theorem 303
Coefficient function 681
Coefficients of linear combination 129
Coefficients of matrix 503
Coefficients of polynomial 98 101
Coerasable 805
Cofinal 52
Cohomology 288 302 303 549 764
Cohomology of groups 826
Cokemel 119 133
Column, operation 154
Column, rank 506
Column, vector 503
Commutative 4
Commutative, diagram ix
Commutative, group 4
Commutative, ring 83 84 86
Commutator 20 69 75
Commutator subgroup 20 75
Commutator subgroup of SL(n) 539 541
Commute 29
Compact, Krull topology 329
Compact, spec of a ring 411
Complete, family 837
Complete, field 469
Complete, ring and local ring 206
| Completely reducible 554
Completion 52 469 486
COMPLEX 445 761 765
complex numbers 272
Component 503 507
Component of a matrix 503
Composition of mappings 85
Compositum of fields 226
Conjugacy class 673
Conjugate elements of a field 243
Conjugate elements of a group 26
Conjugate, embeddings 243 476
Conjugate, fields 243 477
Conjugate, subgroups 26 28 35
Conjugation 26 552 570 662
Connected 411
Connected sum 6
Connection 755
Constant polynomial 175
Constant term 100
Content 181
Contragredient 665
Contravariant functor 62
Convergence 206
Convolution 85 116
coordinates 408
Coproduct 59 80
Coproduct of commutative rings 630
Coproduct of groups 70 72
Coproduct of modules 128
Correspondence 76
Coset 12
Coset, representative 12
Countable 878
Covariant functor 62
Cramer’s Rule 513
Cubic extension 270
Cuspidal 318
Cycle in homology 767
Cycle in permutations 30
Cyclic, endomorphism 96
Cyclic, extension 266 288
Cyclic, group 8 23 96 830
Cyclic, module 147 149
Cyclic, tower 18
Cyclotomic, field 277—282 314 323
Cyclotomic, polynomials 279
Davenport theorem 195
de Rham complex 748
Decomposable 439
Decomposition, field 341
Decomposition, group 341
Dedekind, defined 710 769
Dedekind, determinant 548
Dedekind, ring 88 116 168 353
Definite form 593
Degree of extension 224
Degree of morphism 765
Degree of polynomial 100 190
Degree of variety 438
Degree, Weierstrass 208
Deligne — Serre theorem 319
Density theorem 647
Density theorem, jdenumerable set 875
Dependent absolute values 465
Derivation 214 368 746 754
Derivation, over a subfield 369
Derivation, universal 746
Derivative 178
Derived functor 791
Descending chain condition 408 439 443 661
Determinant 513
Determinant of cohomology 738
Determinant of linear map 513 520
Determinant of module 735
Determinant of Witt group 595
Determinant, ideal 738 739
Diagonal element 504
Diagonalizable 568
Diagonalized form 576
Difference equations 256
Differential 747 762 814
Dihedral group 78 723
Dimension in homology 806 811 823
Dimension of character 670
Dimension of module 146 507
Dimension of transcendental extension 355
Dimension of vector space 141
Dimension, shifting 805
Direct, limit 160 170 639
Direct, product 9 127
Direct, sum 36 130 165
Directed family 51 160
Discrete valuation ring 487
Discriminant 193 204 325
Distinguished extensions of fields 227 242
Distinguished extensions of rings 335 291
Distinguished polynomials 209
Distributivity 83
Divide 111 116
Divisible 50
Division ring 84 642
Dolbeault complex 764
Dominate (polynomials) 870
Double coset 75 693
Doubly transitive 80
Dual, basis 142 287
Dual, group 46 145
Dual, module 142 145 523 737
Dual, representation 665
Effective character 668 685
Eigenvalue 562
Eigenvector 562 582—585
Eisenstein criterion 183
Elementary, divisors 153 168 521 547
Elementary, group 705
Elementary, matrix 540
Elementary, symmetric polynomials 190 217
Elimination 391
Elimination, ideal 392
Embedding 11 120
Embedding of fields 229
Embedding of rings 91
Endomorphism 10 24 54
Endomorphism of cyclic groups 96
Enough, injectives 787
Enough, T-exacts 810
Entire 91
Entire, functions 87
Epimorphism 120
Equivalent, norms 470
Equivalent, places 349
Equivalent, valuations 480
Erasable 800
Euclidean algorithm 173 207
Euler characteristic 769
Euler phi function 94
Euler — Grothendieck group 771
Euler-Poincare, characteristic 769 824
Euler-Poincare, map 156 433 435 770
Evaluation 98 101
Even permutation 31
Exact 15 120
Exact for a functor 619
Exact, sequence of complexes 767
Expansion of determinant 515
Exponent of a field extension 293
Exponent of a group 23
Exponent of a module 149
Exponent of an element 23 149
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