Bruck R.H. — A survey of binary systems :: Электронная библиотека попечительского совета мехмата МГУ

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Bruck R.H. — A survey of binary systems

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Название: A survey of binary systems

Автор: Bruck R.H.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1958

Количество страниц: 185

Добавлена в каталог: 13.04.2013

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Предметный указатель

$f_{i}$ function      148
$\mathfrak{B}$ -condition      77
$\mathfrak{E}$ ( , ) condition      77
$\mathfrak{L}$ () set      150
$\mathfrak{L}$ , $\mathfrak{L}’$ properties      92 93
Add      27
Adjoint      119
Algebra      21
Algebra (bibliography)      163 178
Amalgamated      8
Associative law      23
Associative systems (bibliography)      177
Associative, power      59 64 87
Associator      13
Associator subloop      138
Autctopism      112
Automorphism      3
Automorphism group      88
Automorphism, centre      72
Automorphism, inner      64
Automorphism, pseudo      113
Automorphism, semi      116
Binary operation      1
Cancellation law      8
Cancellation semigroup      26
centralizer      66
Centre      57
Centre $\Omega$ -isomorphism      74 75
Centre automorphism      72
Centre,       95
Centre,       94
Centre, Moufang      94
Chain condition      45
Chain, $\Omega$       67
Chain, chief      67
Chain, divisor      4
Chain, isomorphic $\Omega$       67
Chain, length of      67
Chain, refinement of      67
Characteristic subloop      86
Class argument      141
Closure      119
Closure operation      62
Cogroup      41 43
Commutator      13 70
Commutator-associator subloop      68
Commutator-associator subquasigroup      13
companion      113
Compatible      1
Composition chief system      105
Composition series      67
Congruence      22
Conjugate class      43 63
Conjugate, right      43
Conjugate, self      63
Core      120
Coset      61
Coset expansion      92
Decomposition, direct      72
Decomposition, free      87
Decomposition, refinement of      75
Dedekind’s Law      35
Di-associative      60 87 92
Disjoint      1
distributor      94 141
Division, left      8
Divisionsystem, left      91
Divisor-chain      4
Divisor-chain, length of      4
Endomorphism      3
Endomorphism, $\Omega$       65
Endomorphism, centralizing      68
Endomorphism, normal      68
Endomorphism, orthogonal      68
Endomorphism, semi      116
Endomorphism, zero      68
Enumeration      99
EQUIVALENCE      22
Equivalence class      22 49
Equivalence relation      22
Equivalence, commuting      22
Equivalence, normal      90
Extension      2 103
Extension chain      2
Extension, complete      2
Extension, open      2
Extension, proper      104
Factor, nontrivial free      87
Factor, principal      49
Fitting’s Lemma      82
Flock      40
Frattini subloop      97
Free basis      5
Free basis of $\mathfrak{C}$ -loop      17
Free decomposition      6 7 14 15 16 17 86
Free halfgroupoid      5
Free halfquasigroup      10
Free over      3
Free product      6
Free product, generalized      6
Free representation theorem      5
Free semigroup      37
Free set of generators      10
Freely generated      3
Generate      2
Generatefreely      3
Group      28
Group (bibliography)      178
Group with zero      44
Group, Burnside      28
Group, covering      36
Group, inner mapping      61
Group, mixed      35
Group, multiplication      54
Group, polyadic      21 36
Group, transitive automorphism      88
Groupoid      1
Groupoid (bibliography)      166 178
Groupoid with the left (right) inverse property      111
Groupoid, Brandt      34
Groupoid, crossed-inverse      111
Halfalgebra      21
Halfgroupoid      1
Halfgroupoid, amalgamated      8
Halfgroupoid, closed      2
Halfgroupoid, compatible      1
Halfgroupoid, disjoint      1
Halfgroupoid, intersecting      2
Halfgroupoid, prime in      4
Halfgroupoid, rank of      6
Halfgroupoid, union of      1
Halfloop      15
Halfquasigroup      9
Holomorph      41
Homomorphism      3
Homomorphism of loops      60
Homomorphism of quasigroups      90
Homomorphism, $\Omega$       65
Homomorphism, extend      3
Homomorphism, induce      3
Homomorphism, kernel of      59 60
Hypergroup      41
Ideal      25 44
Ideal, complementary      49
Ideal, left, right      44
Ideal, maximal      45
Ideal, minimal      45
Ideal, principal      49
Idempotent      25 35 44
Idempotent semigroup      50

Idempotent, primitive      44
Identity, left, right      15 41
Identity, Moufang      115
Image, inverse      24 63
Image, loop      91
Imbeddable      7
Imbedding      7
Imbedding, homomorphic      32
Inner mapping      61
Innerautomorphism      64
Intersecting collection      2
Intersection      2
Invariant of principal isotopy      57
Invariant, right      43
Inverse      28
Inverse image      24 63
Inverse property      59 94 111
Inverse property, crossed      111
Inverse semigroup      25
Inverse, relative      25
Irreducible      66
Isomorphism      5
Isomorphism, $\Omega$       65
Isomorphism, centre $\Omega$       74 76
Isomorphism, exchange      76
Isotopy      20 56
Isotopy, geometry and      59
Isotopy, invariants of principal      57
Isotopy, noninvariants of principal      58
Isotopy, principal      56
J divisor-chain, finite      4
Jordan - H $\ddot{o}$ lder theorem      67 90
Kernel of homomorphism      59 60
Kernel of mixed group      35
Kernel, quasinormal      91
Lagrange’s Theorem      92 93
Local -loop      105 157
Local property      102 157
Loop      15
Loop (bibliography)      166 178
Loop image      91
Loop,       87 99
Loop, $SD_{f^{-}}$ , $SD_{f}$ , $SN_{f^{-}}$       108
Loop,       105 157
Loop, $\mathfrak{C}$       17
Loop, additive, multiplicative, of a plane      20
Loop, Cayley      88
Loop, commutative Moufang      130
Loop, crossed-inverse      112
Loop, di-associative      60 87 92
Loop, free $\mathfrak{C}$       17
Loop, hamiltonian      87
Loop, local       105 157
Loop, Moufang      58 110 115
Loop, operator      65
Loop, order-simple      110
Loop, ordered      108
Loop, quotient      61
Loop, simply ordered      108
Loop, totally symmetric      58
Loop, transfinitely upper -nilpotent      95
Loop, upper -nilpotent      95
Loop, with the inverse property      111
Loop, with transitive automorphism group      88
M $\ddot{o}$ bius fuction      100
Maximal associative subset      118
Minimal condition for ideals      45
Moufang centre      94
Moufang configuration      60 120
Moufang element      113
Moufang identity      115
Moufang loop      58 110 115
Moufang loop, commutative      130
Moufang nucleus      94
Moufang Theorem      117
Multigroup      41
Multigroup (bibliography)      169 179
Multigroupoid      41
Multigroupoidwith multiplicity      42
Net      19 59
Net, additive, multiplicative      20
Net, hexagonal      59
Net, order of      19
Nil radical      45
Nil subset      44
Nil,       45
Nilpotency      44 94
Nilpotency function      94
Nilpotency of loops      94
Nilpotency,       45
Nilpotency,       95
Nilpotency, central      94 98
Nilpotency, local central      105 157
Nilpotency, nuclear      94
Nilpotency, transfinite       95
Non-generator      97
Nonsingular, left, right      54
Normal endomorphism      68
Normal equivalence      90
Normal subloop      60
Normal subsemigroup      24
Normal subset      24
Normal system      91
Nucleus Moufang      94
Nucleus, left, middle, right      43 57
Operation of a cardinal on a set      21
Operation, -ary, unary, binary, ternary      21
Operation, closure      62 119
Operation, finitary      21
Operation, infinitary      21
Operation, range of      1
Operator      65
Operator loop      65
Order of a halfgroupoid      1
Order of a net      19
Orthogonal complement      68
Orthogonal endomorphism      68
Plane, affine      20
Plane, degenerate      18
Plane, free      19
Plane, partial      17
Plane, projective      18
Plane, rank of      19
Power-associative      60 64 87
Prime in      4
primitive class      22
Product, direct      72
Product, free      6
Product, outer direct      72
Projection      68
Quasigroup      8
Quasigroup (bibliography)      166 178
Quasigroup, rank of      11
Quasiregular      27
Radical      82
Radical, nil      45
RANGE      1
Rank of a free halfgroupoid      6
Rank of a free quasigroup      11
Rank of a projective plane      19
Refinement of a direct decomposition      75
Refinement of an $\Omega$ -chain      67
Refinement Theorem      67 77
Regular      25 52
Regular on the left      27
Reidemeister figure      88
Relation, equivalence      22
Relation, identical      16
Schreier refinement theorem      67
Schur’s lemma      66

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