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| Lang S. — Algebra |
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| Предметный указатель |
Moebius inversion 116 254
Monic 175
Monoid 3
Monoid, algebra 106 126
Monoid, homomorphism 10
Monomial 101
Monomorphism 120
Morita’s theorem 660
Morphism 53
Morphism of complex 765
Morphism of functor 65 625 800
Morphism or representation 125
Multilinear map 511 521 602
Multiple root 178 247
Multiplicative, function 116
Multiplicative, subgroup of a field 177
Multiplicative, subset 107
Multiplicity of character 670
Multiplicity of root 178
Multiplicity of simple module 644
Nakayama’s Lemma 424 661
Natural transformation 65
Negative 449
Negative, definite 578
Newton approximation 493
Nilpotent 416 559 569
Noether normalization 357
Noetherian 186 210 408—409 415 427
Noetherian, graded ring 427
Non-commutative variables 633
Non-degenerate 522 572
Non-singular 523 529
Norm 284 578 637
Norm on a finitely generated abelian group 166
Norm on a vector space 469
Normal, basis theorem 312
Normal, endomorphism 597
Normal, extension 238
Normal, subgroup 14
Normal, tower 18
normalizer 14
Northcott theorems 864
Null, sequence 52
Null, space 586
Nullstellensatz 380 383
Occur 102 176
Odd permutation 31
One-dimensional, character 671
One-dimensional, representation 671
Open complex 761
Open set 406
Operate on a module 664
Operate on a set 25 76
Operate on an object 55
Orbit 28
Orbit, decomposition formula 29
Order at a valuation 488
Order at p 113 488
Order of a group 12
Order of a zero 488
Ordering 449 480 878
Ordinary tensor product 630
Orthogonal, basis 572—585
Orthogonal, element 48 144 572
Orthogonal, group 535
Orthogonal, map 535
Orthogonal, sum 572
Orthogonality relations 677
Orthogonalization 579
Orthonormal 577
Over a map 229
p-adic, integers 51 162 169 488
p-adic, numbers 488
p-class 706
p-conjugate 706
p-divisible 50
p-elementary 705
p-group 33
p-regular 705
p-singular 705
p-subgroup 33
Pairing 48
Parallelogram law 598
Partial fractions 187
Partition 79
Partition, function 211
Perfect 252
Period 23 148
Periodicity of Clifford algebra 758
Permutation 8 30
Perpendicular 48 144 522
Pfaffian 589
Pic or Picard group 88 126
Place 349 482
Poincar 6
Poincar, series 211 431
Point in a field 408
Point of algebraic set 383
Polar decomposition 584
Polarization identity 580
Pole 488
Polynomial 97
Polynomial, algebra 97 633
Polynomial, function 98
Polynomial, invariants 557
Polynomial, irreducible 175 183
Polynomial, Noetherian 185
Polynomials 181 182
Pontijagin dual 145
Positive 449
Positive, definite 578 583
Power map 10
Power series 209
Power series, factorial 209
Power series, Noetherian 210
Power series, root 301
Power series, root of unity 277 278
Primary, decomposition 422
Primary, ideal 421
Primary, module 421
Prime, element 113
Prime, field 90
Prime, ideal 92
Prime, ring 90
Primitive, element 243 244
Primitive, group 80
Primitive, operation 79
Principal, homomorphism 418
Principal, ideal 86 88
Principal, module 554 556
Product in category 58
Product of groups 9
Product of modules 127
Product of rings 91
Profinite 51
Projection 388
Projective, module 137 168 848 850
Projective, resolution 763
Projective, space 386
Proper ix
Proper, congruence 492
Pull-back 61
Purely inseparable, element 249
Purely inseparable, extension 250
Push-out 62 81
Quadratic, extension 269
Quadratic, form 575
Quadratic, map 574
Quadratic, symbol 281
Quadratically closed 462
| Quaternions 9 545 723 758
Quillen — Suslin theorem 848
Quotient, field 110
Quotient, ring 107
Radical of a ring 661
Radical of an ideal 388 417
Radical of an integer 195
Ramanujan power series 212
Ramification index 483
Rank 506
Rank of a matrix 506
Rank, and 722
Rank, vector 503
Rational, conjugacy class 276 326 725
Rational, element 714
Rational, function 110
REAL 451
Real, closed 451
Real, closure 452
Real, place 462
Real, zero 457
Reduced, decomposition 422 443
Reduced, polynomial 177
Reduction, criterion 185
Reduction, map 99 102
Reduction, mod p 623
Reduction, modulo an ideal 446 623
Refinement of a tower 18
Regular, character 675 699
Regular, extension 366
Regular, module 699 829
Relations 68
Relative invariant 171 327
Relatively prime 113
Representation 554
Representation of a group 55 317 664
Representation of a ring 553
Representation, functor 64
Representation, sequence 850
Representation, space 667
Representation, subgroup 9
Representation, valuation 465
Residue class 91
Residue class, degree 422 483
Resolution 788 801 819
Resultant 200 398 410
Resultant, system 403
Resultant, variety 393
Ribet 319
Rieffel’s theorem 655
Riemann surface 275
Riemann — Roch 212 218 220 258
Right, coset 12 75
Right, derived functor 791
Right, exact functor 791 798
Right, ideal 66
Right, module 117
Rigid 275
Rigidity theorem 276
Ring 86 146 521
Ring of fractions 107
Ring, homomorphism 88
Root 175
Root of unity 177 276
Row, operation 154
Scalar product 571
Schanuel, conjecture 873
Schanuel, lemma 841
Schreier’s theorem 22
Schroeder — Bemstein theorem 885
Schwarz inequality 578 580
Section 64 792
Self-adjoint 581
Semidirect product 15 76
Semilinear 532
Seminorm 166 475
Semipositive 583 597
Semisimple, endomorphism 569 661
Semisimple, module 554 647 659
Semisimple, representation 554 712
Semisimple, ring 651
Separable, closure 243
Separable, degree 239
Separable, element 240
Separable, extension 241 658
Separable, polynomial 241
Separably generated 363
Separating transcendence basis 363
SEQUENCE 875
Serre’s conjecture 848
Serre’s conjecture, theorem 844
Sesquilinear form 532
Shafarevich conjecture 314
Sheaf 792
Sign of a permutation 31 77
Simple, character 669
Simple, group 20
Simple, module 156 554 643
Simple, ring 653 655
Simple, root 247
Simplicity of SL 539 542
Size of a matrix 503
Skew symmetric 526
Snake lemma 158 169 614—621
Snyder’s proof 220
Solvable by radicals 292
Solvable, extension 291 314
Solvable, group 18 293 314
Spec of a ring 405 410
Special linear group 14 52 59 69 541 546 547
Specialization 384
Specializing 101
Spectral, sequence 815—825
Spectral, theorem 581 583 585
Split exact sequence 132
Splitting field 235
Square, group 9 77 270
Square, matrix 504
Square, root of operator 584
Stably free 840
Stably free, dimension 840
Stably isomorphic 841
Stalk 161
Standard, alternating matrix 587
Standard, complex 764
Steinberg theorem 726
Stewart — Tijdeman 196
Strictly inductively ordered 881
Stripping functor 62
Sturm’s Theorem 454
Subgroup 9
Submodule 118
Submonoid 6
Subobject 134
Subring 84
Subsequence 876
subspace 141
Substituting 98 101
Suijective ix
Super, algebra 632
Super, commutator 757
Super, product 631 751
Super, tensor product 632 751
Supersolvable 702
Support 419
Sylow group 33
Sylvester’s theorem 577
Symmetric, algebra 635
Symmetric, endomorphism 525 585 597
Symmetric, form 525 571
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