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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume I: Foundations of Mathematics: The Real Number System and Algebra |
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| Предметный указатель |
Relation(s), transitive 63
Relation(s), universal 62
Relation(s), void 62
Relative complement 499
Relative consistency 31
Relative product 62
Relatively complemented 499
Relevant expression 76n
Relevant proposition 29
Remainder theorem (Chinese) 391
Remainder: reduced 174
Replacement axiom 60
Representation 220
Representation, degree of a 220
Representation, regular 223
Representation, transitive 222
Representing property 535
Residue(s): class ring 342 381
Residue(s): classes 109 186 341 461
Residue(s): quadratic 399
Residue(s): quadratic, Euler criterion for a 400
Residue(s): system, complete 381
Restriction against circularity 43
Resultant 349
Riemann, sphere 472
Right cosets 186
Right difference 161
Right ideals 357
Right inverse 167n2
Right residue classes 186
Rigid mapping 172n
Ring(s) 116
Ring(s), additive group of a 318 357
Ring(s), Boolean 69
Ring(s), commutative 117 317
Ring(s), Euclidean 332 361
Ring(s), extension 297
Ring(s), factorization theorem for 343
Ring(s), homomorphism theorem for 342
Ring(s), integrally closed 403
Ring(s), multiplicative semigroup of a 357
Ring(s), Noetherian 339
Ring(s), of endomorphisms 116
Ring(s), of integers 120
Ring(s), of linear transformations 249
Ring(s), ordered 120
Ring(s), polynomial 299 304
Ring(s), power-series 311
Ring(s), principal ideal 339
Ring(s), quotient 368
Ring(s), residue class 342 381
Ring(s), theory 28
Ring(s), unique factorization 331
Rodrigues, formula for rotations 477
Roof 529
Root 302n15
Root, exponent of a 445
Root, nth 148
Root, of unity 425
Root, primitive 399 427
Root, square 148
Rotation(s) 205
Rotation(s), dilative 457
Rotation(s), dilative, Hermitian 469
Rotation(s), Hermitian 468
Rotation(s), of the plane 456
Rotation(s), of the sphere 472
Rotation(s), Rodrigues formula for 477
Rotatory reflections 206
Rule(s): Horner's 294 295
Rule(s): of an algorithm 33
Rule(s): of inference 41 43
Rule(s): of separation 41
Rule(s): power 200
Russell and A. N. Whitehead 42
Russell antimony 59 81
Russell vicious circle principle 535
Russell, Bertrand 22 51
Scalar part 475
Scalar product 234 266 269
Scalars, domain of 235
Schema: axiom 26 34
Schema: induction 75
Schnirelmann 405
Schnirelmann, basis theorem of 407
Schouten 246 262
Schreier, Artin-, theorem of 527
Science, abstract 27
Science, natural 27
Second axiom for unions 60
Second Cantor diagonal procedure 55
Second domain 62
Second language layer 136n74
Segment(s) 102 156 520
Segment(s), initial 156 532
Segment(s), maximal 157
Segment(s), proper 156
Self-contradictory system of axioms 31
Self-dual 501
Semantic(s) 20
Semantic(s), antinomy 81
Semantic(s), consistency 31
Semi-orderings 63
Semilattice 487
Semimodular: above 503
Semimodular: below 503
Sense (Sinn) 10
Separability, criterion for 424
Separable extensions 422
Separable polynomial 422
Separation, rule of 41
Sequence(s) 64
Sequence(s), Cauchy or fundamental 139
Sequence(s), diagonal 152
Sequence(s), fundamental, of Cantor 133
Sequence(s), limit of a 132
Sequence(s), of numbers 104
Sequence(s), zero 140
Series of fields and groups 438
Series, power- 308
Series, power-, field and ring 311
Series: composition 216 354
Set(s) 50
Set(s), -lattice 499
Set(s), -orders 523
Set(s), algebra of 53
Set(s), axiom for, with one element 60
Set(s), cardinality of a 54
Set(s), directed 64
Set(s), element of a 51
Set(s), empty 52 103
Set(s), empty, axiom for the 60
Set(s), equivalence of 103
Set(s), extension of a 51
Set(s), field of 53
Set(s), finite (Dedekind definition) 103n21
Set(s), formation, operator of 12
Set(s), ground 62
Set(s), power 52 54 485
Set(s), power, axiom 60
Set(s), universal 52 57
Set(s), universal, antinomy of the 57
Set-theoretic connectives 487
Sets, class in 58
Sets, naive or intuitive 51 534
Sets, ordered 50 56 522
Sets, ordered, linearly 522
Sets, ordered, totally 522 533
Sets, ordered, well- 153 155 532
Sets, theory of 3—4 9
| Sharpened high chain principle 530n
Signature of a form 272
Signs, function 12 15
Similar 56 221 226 262
Similarity 156
SIMPLE 228
Simple group 196
Simple properly 196
Skew field 235 324 526n
Skew field of quaternions 470
Skew-symmetric matrix 314
Skew-symmetric tensor 276
Skolem, and Lowenheim, theorem of 71
Smallest splitting field 413
Smallest splitting field, uniqueness theorem for 415
Solutions, fundamental system of 257
Solvability, by radicals 452
solvable 216
Space 169
Space, dual 263
Space, image 247
Space, metric 270
Space, vector 233 238 526n
Space, vector, dual 234
Spanned subspace 243
Special continuum hypothesis 60
Sphere, Riemann 472
Sphere, rotations of the 472
Spiral motions 205
Splitting field 413
Splitting field, in the wider sense 413
Splitting field, smallest 413
Splitting field, smallest, uniqueness theorem for 415
Square matrix 177
Square root 148
Square: -free 388
Statements, valid 516
Stoics 14
Structure(s) 5 508 515 516
Structure(s), constants 402—403n37
Structure(s), elementary-arithmetical 521
Structure(s), elementary-logical 521
Structure(s), metric 270
Structure(s), nonelementary 521
Structure(s), problem for groups 191
Structure(s), pure-elementary 521
Structure(s), type 516
Sturm chain 463
Sturm theorem 463
Subband(s) 492 517
Subconfiguration 517
Subdeterminant, algebraic complement of a 283
Subfield 297nll
Subgroup(s) 184
Subgroup(s), admissible 518
Subgroup(s), congruence modulo a 380
Subgroup(s), criterion for 184
Subgroup(s), improper 184
Subgroup(s), index of a 186
Subgroup(s), intersection of 436
Subgroup(s), invariant 194
Subgroup(s), maximal 186
Subgroup(s), minimal 186
Subgroup(s), normal 188 194 518
Subgroup(s), proper 184
Subgroup(s), trivial 184
Subideal 339n
Subject variables 11
Subject(s) 12 15 21
Sublattice 492 517
Subring 322 338
Subset 52
Subset, proper 52 95n5
subspace 526n
Subspace, spanned 243
Subspace, vector 243 526n
Substitution 168 300
Successive application 115
Successor 38 56 93 94
Successor, relation 32
SUM 133
Sum function 38
Sum of endomorphisms 114
Sum of numbers 95
Sum of ordinal numbers 159
Sum, digital 385 386
Sum, direct, of the ideals 392
Summation convention, Einstein 239
Summatory function 371 388
Superfluous elements 497
Suzuki, M. 519
Sylow p-groups 220
Sylow theorem 219
Sylvester determinant 349
Sylvester, law of inertia 272
Symbol(s): fin 134
Symbol(s): Jacobi 400
Symbol(s): Kronecker 245
Symbol(s): logical 485
symmetric 63 108 270 306
Symmetric group 171
Symmetric polynomials 307
Symmetric, elementary: functions 307n23
Symmetric, skew-, matrix 314
Symmetric, skew-, tensor 267
Symmetry 29
Syntactic antinomy 81
Syntactic consistency 31
Syntax 20
Tarski, A. 20
Tautology 23 24—25
Tensor product 235 273
Tensor, covariant 264
Tensor, fundamental 270
Tensor, skew-symmetric 276
Terms, lowest 360
Tertium поп datur 43 47 49
Tetartohedrism 209
Thales 27
Theorem: Artin — Schreier 527
Theorem: Bernstein, equivalence 54
Theorem: Bezout 354
Theorem: binomial 295
Theorem: Cantor fundamental 163
Theorem: chain, of Dedekind 504
Theorem: Chinese remainder 391
Theorem: completeness, of Godel 42
Theorem: factorization, for rings 343
Theorem: Fermat 382
Theorem: for complex numbers, fundamental algebraic 467
Theorem: for complex numbers, fundamental topological 467n8
Theorem: fundamental, for cyclic groups 192
Theorem: fundamental, of algebra 467
Theorem: incompleteness (Goedel) 72
Theorem: intermediate value 462
Theorem: isomorphism 214
Theorem: Jordan — Hoelder 216 354 504
Theorem: little, of Desargues 482
Theorem: of Frobenius 478
Theorem: of Lowenheim and Skolem 71
Theorem: prime number 406
Theorem: Pythagorean 4 27
Theorem: Schnirelmann basis 407
Theorem: Sturm 463
Theorem: Sylow 219
Theorem: Uniqueness, for smallest splitting fields 415
Theorem: well-ordering 56 525
Theorem: Wilson's 384
Topological: group 232
Topological: theorem for complex numbers, fundamental 467n8
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