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Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume I: Foundations of Mathematics: The Real Number System and Algebra
Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume I: Foundations of Mathematics: The Real Number System and Algebra



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Название: Fundamentals of Mathematics, Volume I: Foundations of Mathematics: The Real Number System and Algebra

Авторы: Behnke H., Bachmann F., Fladt K.

Аннотация:

Volume I of a unique survey of the whole field of pure mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 549

Добавлена в каталог: 26.02.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Lambda$-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
1 2 3 4 5 6 7
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