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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 |
Congruence(s), pure 399
Congruence(s), relation 65 514
Congruent 270
Conjecture: Fermat 11—12 37 398
Conjecture: Goldbach 10 76 405
Conjugate algebraic elements 431
Conjugate Cayley number 481
Conjugate fields 437
Conjugate quaternion 475
Conjugate transposed matrix 270
Conjugate(s) 183
Conjugate(s), system of 402n36
Conjugate, complex 461
Conjunction 12
Connectives: lattice-theoretic 487
Connectives: logical 487
Connectives: set-theoretic 487
Connex 63
Connexity 522
Consequence 8 20 24 46
Consistency 6 109
Consistency, relative 31
Consistency, semantic 31
Consistency, syntactic 31
Consistent algorithm 39
Constant function 291
Constants: propositional 12
Constants: structure 402—403n37
Constructibility of a regular polygon 454
Constructive (point of view) 7
Constructivist 534—535
Constructivist school 7—8 40
Continuous function 462
Continuum 55
Continuum, hypothesis 60
Continuum, hypothesis, special 60
Contradiction 23 80
Contragredient 264
Contraposition 47
Contravariant vector 264
Convention, Einstein summation 239
Conventionalism 6
Convergence criterion (Cauchy) 467n8
Convergent of a continued fraction 373
Converse relation 62
coordinates 240
Coprime 332
Coset: left 186
Coset: right 186
Countable 55 151
Countable at most 55
Countably infinite 151n90
Covariant tensor 264
Covariant vectors 264
Criterion(a): convergence (Cauchy) 467n8
Criterion(a): for a quadratic residue function (Euler) 400
Criterion(a): for divisibility 385
Criterion(a): for multiplicity of zeros 426
Criterion(a): for separability 424
Criterion(a): for subgroups 184
Criterion(a): irreducibility (Eisenstein) 347
Crystallography 204
Cube, duplication doubling of 417
Curry 40
Cut, Dedekind 50 133 135
CYCLE 224
Cyclic 191
Cyclic groups 191
Cyclic groups, fundamental theorem for 192
Cyclotomic: field 405
Cyclotomic: polynomial 428 430
De Moivre, formula of 458
Decidable 36
Decimal, infinite 130
Decomposition into partial fractions 368
Decomposition, canonical 225
Dedekind cut 50 133 135
Dedekind, chain theorem of 504
Dedekind, definition of infinity 54
Dedekind, Richard 72 403 448 483 488
Deduction 41
Deficient number 371
Definite, positive 273
Definition 20—21
Degree 299
Degree of a representation 220
Degree of an algebraic extension 420
Denominator 122
Denominator, lowest common 360
Denotation (bedeutung) 10
density 407
Dependent, linearly 240
Derivation 41
Derivation, algorithmic 53
Derivative 303
Derivative of a polynomial 423
Desargues, little theorem of 482
Description operator 12 18
Determinant(s) 235 279
Determinant(s), expansion of a 282
Determinant(s), multiplication of 280
Determinant(s), Sylvester 349
Diagonal procedure (Cantor's) 152
Diagonal procedure (Cantor's), first and second 55
Diagonal sequence 152
Diagonal: form of a matrix 260
Diagram(s) 186
Diagram(s) of Hesse 485
Diagram(s) order 485
Dickson, L.E. 448
Difference: left 161
Difference: right 161
Digital sum 385
Digital sum, alternating 385
Digital sum, generalized 385
Dilatation zero 456
Dilatation(s) of the plane 456
Dilative rotations 457
Dilative rotations, Hermitian 469
DIMENSION 240 505
Dimensional equation 505
Dirac,  -function 5
Direct product 198 493
Direct product of groups 394
Direct sum of (the ideals) 392
Directed 64
Directed set 64
Dirichlet 406
Dirichlet pigeon-hole principle 102 463
Discriminant 352 402
Disjoint 52
Disjunction 13
Distributions 5
Distributive lattice 68 489
Distributive laws 53 99 115
Distributive laws, infinite 490
Divisibility: criteria for 385
Divisibility: fundamental lemma of the theory of 359
Division algebra(s) 402—403n37 477
Division algebra(s), associative 478n17
Division algebra(s), of finite rank 478
Division: two-sided 180
Divisor of zero 119 293 322
Divisor of zero, nilpotent 342
Divisor(s): common 358
Divisor(s): complementary 356
Divisor(s): greatest common 332 358
Divisor(s): prime 358
Divisor(s): proper 357
Divisor(s): trivial 357
| Divisor-chain 330
Divisor-chain, condition 360
Divisor-chain, proper 330
Domain(s) 62
Domain(s), first 62
Domain(s), fundamental 411
Domain(s), image 247
Domain(s), integral 119n47 323
Domain(s), of a function 50
Domain(s), of individuals 21
Domain(s), of integrity 323
Domain(s), of positivity 120 464 527
Domain(s), of scalars 235
Domain(s), of transitivity 221
Domain(s), operator 511
Domain(s), second 62
Dual 487
Dual, axiom 68
Dual, group 483 488 517
Dual, self- 501
Dual, space 263
Dual, vector space 234
Duality, principle of 68
Duplication doubling of the cube 417
Dyadic fractions 130n60
Echelon matrix 259
Eigenvalues 286
Eigenvectors 286
Einstein, summation convention of 239
Eisenstein, irreducibility criterion of 347
Element(s) 50
Element(s), axiom for sets with one 60
Element(s), conjugate algebraic 431
Element(s), exponent of a group 193
Element(s), G, order of the 193
Element(s), greatest 490 523
Element(s), greatest common 0
Element(s), identity 167
Element(s), inverse 111
Element(s), least 490 523
Element(s), least common upper 486
Element(s), lower 486
Element(s), maximal 164 523
Element(s), minimal 523
Element(s), neutral 111 167 237
Element(s), of a set 51
Element(s), order of a group 193
Element(s), permutable 168
Element(s), prime 403
Element(s), superfluous 497
Element(s), unit 66 116 167 179 321 490
Element(s), unity 321
Element(s), zero 179 490
Element(s), “imaginary” 448
Elementary ornament 204
Elementary predicate logic 73
Elementary symmetric functions 302n23
Elementary symmetric polynomials 307
Elementary: -arithmetical structure 521
Elementary: -logical structure 521
Elimination 353
Elimination, assumption- 45
Elimination, ideal 354
Empty relation 62
Empty set 52 103
Empty set, axiom for 60
Empty word 231
Endomorphism(s) 114 128 512
Endomorphism(s), monotone 146
Endomorphism(s), multiplication of 115
Endomorphism(s), ring of 116
Endomorphism(s), sum of 114
Entire rational function 292
Entire rational function, in the sense of algebra 301
Entire rational function, in the sense of analysis 301
Entire rational function, of n arguments 305
Enumerability 35
Enumerable, recursively 33 35
Equality 108
Equality of classes 58
Equality of value 122
Equation(s), characteristic, of a matrix 286
Equation(s), class 218
Equation(s), dimensional 505
Equation(s), Pell 397
EQUIVALENCE 14
Equivalence, class 65
Equivalence, of matrices 254
Equivalence, of sets 103
Equivalence, relations 29 65 108
Equivalence, theorem (Bernstein) 54
Equivalent 54
Euclid 28
Euclidean algorithm 32 332 365
Euclidean rings 332 361
Euler criterion for a quadratic residue 400
Euler function 382
Even transpositions 227
Excluded middle, law of 8
Existence-introduction 48n23
Existential quantifier 17 18
Expansion: Laplace 283
Expansion: of a determinant 282
EXPONENT 445
Exponent of a group element 193
Exponent of a root of unity 445
Exponential function 150
Expression, relevant 76n
Extended matrix 259
Extended predicate logic 23n 42 72
Extension 51
Extension, algebraic 418
Extension, algebraic, degree of an 420
Extension, field 297nll 413
Extension, finite 418
Extension, Galois 420
Extension, normal 420
Extension, of a set 51
Extension, problem 413
Extension, ring 297
Extension, separable 422
Extensionality, principle of 51 58
F-chain 531
Factor 75
Factor group 196
Factor, chain condition 495
Factor, composition 216
Factor, proper 328
Factorization rings, theorem for 343
Factorization rings, unique 331
Factorization, canonical 332
FALSE 10 23
Fermat conjecture 11—12 37 398
Fermat number 372
Fermat theorem 382
Field splitting 413
Field splitting, in the wider sense 413
Field splitting, smallest 413
Field splitting, uniqueness theorem for smallest 415
Field(s) 124 323
Field(s), alternative 481
Field(s), characteristic of a 324
Field(s), composition of 436
Field(s), composition series of 438
Field(s), conjugate 437
Field(s), cyclotomic 405
Field(s), extension (or subfield) 297n11 413
Field(s), finite 440
Field(s), formally real 464 527
Field(s), intersection of 436
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