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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 |
 -introduction 80
A number, an 77
Abelian group 111n33 168
Absolute values 128 310n27 458
Absorption laws 53
Abstract algebra 65 91 92 511
Abstract science 27
Abstraction 5 65
Abundant number 371
Addition 98
Addition, algorithm for 34
Addition, monotonicity of 100
Addition, of integers 111
Addition, of matrices 251
Addition, of transformations 247
Addition, recursive definition of 98n12
Additive group of a ring 318 357
Adjoint 315
Adjunction 411
Admissible subgroups 518
Affine complex plane 468
Aleph-zero 55
Algebra of Logic (Boole's) 42
Algebra(s) 345 402—403n37
Algebra(s), abstract 65 91 92 511
Algebra(s), associative 402—403n37
Algebra(s), Boolean 9
Algebra(s), Cayley 481
Algebra(s), circuit 484 494
Algebra(s), division 402^103n37 478n17
Algebra(s), entire rational function in the sense of 301
Algebra(s), fundamental theorem of 467
Algebra(s), of finite rank 478
Algebra(s), of sets 53
Algebraic complement of a subdeterminant 283
Algebraic congruence 396
Algebraic elements, conjugate 431
Algebraic extension 418 420
Algebraic functions 306
Algebraic integers 330 401
Algebraic manifold 354
Algebraic number 401
Algorithm 7 32 79
Algorithm, consistent 39
Algorithm, Euclidean 32 332 365
Algorithm, for addition 34
Algorithm, for multiplication 34
Algorithm, rule of an 33
Algorithmic derivation 33
Algorithmic proof 33
Alphabet 39
Alternating 314n30
Alternating group 227
Alternating product 235 275
alternative 13
Amicable numbers 372
Analysis: entire rational function in the sense of 301
Analysis: ramified 40
Analytic number theory 406
Angle, trisection of 417
Antiautomorphism 470
Antinomy(ies) 9 51 80
Antinomy(ies), Grelling's 85
Antinomy(ies), of Burali — Forte 57
Antinomy(ies), of the Liar 76 81
Antinomy(ies), of the universal set 57
Antinomy(ies), Russell's 59 81
Antinomy(ies), semantic 81
Antinomy(ies), syntactic 81
Antireflexivity 100
Application, successive 115
Approximation, best 377
Archimedes, axiom of 127n57
Archmidean ordering 127
Argument(s): entire rational function of n 305
Argument(s): from n to n+1 94
Aristotle 10 20 83
Arithmetic 5
Arithmetic, incompleteness of 40
Arithmetization 36
Ars indicandi 49
Ars inveniendi 42 49
Artin-Schreier, theorem of 527
Ascending chain condition 524
assertion 43
Associate(s) 328 356
Associative 98
Associative laws 53
Associative, division algebras 478n17
Associator 481
Assumption(s) 42 43
Assumption(s), -elimination 45
Assumption(s), -introduction 45
At most countable 55
Atom(s) 69 79 80 490
atomic 490
Attribute 21
Aut 13
Autologic 85
Automorphism 148 191 412 512
Automorphism, group 191
Automorphism, group, of the configuration 512
Autonomous notation 10n
Autonomous system of axioms 27 29 67
Axiom of cancellation 181
Axiom of Choice 60 103n20 164 530 534
Axiom of comprehension 58
Axiom of induction 94
Axiom of infinity 60
Axiom(s) 4—5
Axiom(s), autonomous system of 27 29 67
Axiom(s), categorical system of 30
Axiom(s), complete system of 29
Axiom(s), dual 68
Axiom(s), for sets with one element 60
Axiom(s), for the empty set 60
Axiom(s), for unions (first and second) 60
Axiom(s), heteronomous system of 27
Axiom(s), monomorphic system of 30
Axiom(s), Peano system of 93
Axiom(s), power set 60
Axiom(s), replacement 60
Axiom(s), schema 26 34
Axiom(s), self-contradictory system of 31
Axiom(s), system 516
Axiom(s), well-ordering 164
Axiom(s), Zermelo's (of choice) 164
Axiom, of Archimedes 127n57
Babylonians 4 27
Base 129
Basis 242 526
Basis condition 339
Basis integer 402
Basis of an ideal 339
Basis of kth order 405
Basis theorem (Schnirelmann's) 407
Basis vectors 234
Bernays, R. 58
Bernstein, equivalence theorem of 54
Best approximation 377
Betti number 303
Bezout, theorem of 354
Bilinear form 264 268
Bilinear form, Hermitian 271
Bilinear mapping 234
Binary operation 167
Binomial coefficients 295
Binomial theorem 295
Birkhoff, G. 483 520
Birkhoff, Hausdorff — , maximal chain principle 530 533
| Bolzano, Bernard 20
Boole Algebra of Logic 42
Boole, George 174n
Boolean algebra 9
Boolean lattice(s) 67 484 490 495
Boolean ring 69
Bound: greatest lower 68 132 486
Bound: least upper 68 486
Bound: lower 523
Bound: proper upper 523
Bound: upper 486 523
Bound: variable 17 23 60
Bourbaki, N. 510
Brouwer, L.E.J. 6
Burali — Forte, antinomy of 57
Burnside, W. 217
Calculus(i) 9 32
Cancellation, axioms of 181
Cancellation, first rule 319
Cancellation, second rule 323
Canonical decomposition 225
Canonical factorization 332
Cantor diagonal procedure 152
Cantor diagonal procedure (first and second) 55
Cantor fundamental sequences 133
Cantor fundamental theorem 163
Cardinal number(s) 54 94
Cardinality (of a set) 54
Categorical system of axioms 30
Cauchy convergence criterion of 467n81
Cauchy sequences 139
Cayley 223
Cayley algebra 481
Cayley conjugate number 481
Cayley numbers 481
Cayley octaves 481
Center 218 226
centralizer 218
Chain condition: ascending 524
Chain condition: divisor 360
Chain condition: factor 495
Chain condition: high 529
Chain condition: principle 522 530
Chain condition: principle, sharpened 530n
Chain(s) 485 522 529
Chain(s), above and below 524
Chain(s), divisor 330
Chain(s), f- 531
Chain(s), length of a 495
Chain(s), maximal 504
Chain(s), principle, Hausdorff — Birkhoff maximal 530 533
Chain(s), proper 495
Chain(s), Sturm 463
Chain(s), theorem (Dedekind) 504
Characteristic equation of a matrix 286
Characteristic of a field 324
Chatelet 483
Chinese remainder theorem 391
Choice, axiom of 60 103n20 530 535
Choice, axiom of Zermelo 164
Choice, function 535
Church, A. 49
Circle principle (Russell), vicious 535
Circuit algebra 484 494
Circularity, restriction against 43
Class residue 109 341 461
Class residue, left and right 186
Class residue, ring 342 381
Class(es): equality of 58
Class(es): equation 218
Class(es): equivalence 65
Class(es): ideal 404
Class(es): in set theory 58
Class(es): number 56 404
Class(es): universal 59
Classical ideal theory 343
Classical logic 4
Closed 517
Closed interval 499
Coefficients 299 304
Coefficients, binomial 295
Coefficients, comparison of 296
Coefficients, leading 299
Cogredient 264
Column rank of a matrix 253
Combination, linear 239
Common divisor 358
Common divisor, greatest 332 358
Communication 9
Commutative 98
Commutative group 111n33 168
Commutative laws 53
Commutative ring 117 317
Commutator group(s) 197 217
Comparability 522
Comparable 158
Comparativity 65
Comparison of coefficients 296
Complement 52 62 490
Complement, relative 499
Complementary divisor 356
Complementation, laws for 53
Complemented 490
Complemented lattice 68
Complemented relatively 499
complete 487
Complete induction 57 94 117
Complete induction starting from k 101
Complete lattice 138n76 491
Complete ordered module 138
Complete residue system 381
Complete system of axioms 29
Complete system of rules of inference 41
Completeness of predicate logic 42
Completeness theorem (Goedel) 42
Complex conjugate 461
Complex numbers: fundamental algebraic theorem for 467
Complex numbers: fundamental topological theorem for 467n8
Complex numbers: left-multiplication in the domain of 457
Complex plane, affine 468
Complex projective line 471
Complex-product 182 266
Complexes of a group 182
Componentwise multiplication 392
composition 406
Composition configuration 511
Composition factors 216
Composition of fields 436
Composition of groups 436
Composition series 216 354
Composition series of fields 438
Composition series of groups 438
Composition, inner 510
Composition, nonelementary 510
Comprehension, axiom of 58
Computable function 36
Concepts, fundamental 22 26
Condition(s): ascending chain 524
Condition(s): basis 339
Condition(s): divisor-chain 360
Condition(s): factor chain 495
Condition(s): maximal 360
Condition(s): normality 265
Condition(s): orthogonality 265
Configuration(s) 251 508 509
Configuration(s), automorphism group of the 512
Configuration(s), composition- 511
Congruence(s), a subgroup 380
Congruence(s), algebraic 396
Congruence(s), modulo an ideal 341
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