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Higgins P. — Techniques of Semigroup Theory
Higgins P. — Techniques of Semigroup Theory

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Название: Techniques of Semigroup Theory

Автор: Higgins P.

Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 272

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{D}$ (Green’s relation)      15
$\mathcal{H}$ (Green’s relation)      15
$\mathcal{H}$-trivial      21
$\mathcal{K}$ (Green’s relation)      15
$\mathcal{L}$ (Green’s relation)      15
$\mathcal{R}$ (Green’s relation)      15
(u, v)-diagram      74
0-bisimple semigroup      16 22 36
0-direct union      26 42
Absolutely closed semigroup      143
Amalgam      159 165
Amalgam, (weakly, strongly) embeddable      159
Amalgam, core of      159
Amalgam, special      159 160
Amalgamation base (strong, weak)      160 162—163
Amalgamation base (strong, weak), special      160
Amalgamation pair      161 162
Amalgamation property, special      159 161
Amalgamation property, strong      159 161
Amalgamation property, weak      159 161
angle      77
Angle, included edge(s)      77
Angle, included region(s)      77
Angle, interior      77
Angle, sides of      77
Angle, sink-      77 183—184
Angle, source-      77 183—184
Anti-automorphism      11
Anti-homomorphism      11
Anti-isomorphism      11
Anti-representation      11
ARC      69
Arrow (left, right)      60
Automorphism      2
Automorphism of word trees      83
Automorphism, group acting on the left      98
Automorphism, partial      5
Baer — Levi semigroup      14 37 157
Band(s)      2 157
Band(s), (left, right) normal      43
Band(s), 0-rectangular      42
Band(s), commutative      2
Band(s), medial      43
Band(s), normal      43
Band(s), of groups      43
Band(s), of type-T semigroups      37
Band(s), rectangular      2 64 141
Basic products      113
Bimorphism      61
Binary relation(s)      5
Binary relation(s), semigroup of      5
Biorder      60
Biordered set(s)      60—66 110—141
Biordered set(s) of bands      127—130 141
Biordered set(s) of completely regular semigroups      137
Biordered set(s) of eventually regular semigroups      142
Biordered set(s) of regular semigroups      130—133
Biordered set(s), axioms of      111—112
Biordered set(s), isomorphism between      112
Biordered set(s), M-biordered      62 67
Biordered set(s), morphism      61 112 119
Biordered set(s), rectangular      67
Biordered set(s), regular      62 66 137 141
Biordered set(s), solid      135 137 141
Biordered set(s), subset      113 120
Boundary (left, right)      74 177
Brandt semigroup      42 156 165
Bridge      71 217
Cancellative semigroup (left, right)      3 12 29 79
Central element      39
Centre of a tree      69 83
Chain conditions      23
Closed subset of the free group      95
Commutative      2 43 154
Commutative, regular semigroup      40
Commutative, variety      155—156
Complete sequence      136
Completely (0-) simple semigroup      33—37 66 126 141
Completely regular element      4 73
Completely regular semigroup      4 37—41 72 73 157
Completely semisimple      41 59 91 152—153
Component, cyclic      71
Component, even (odd)      209
Component, number      197—199
Component, simple      76
Component, two-sided      74
Congruence(s)      6
Congruence(s), (left, right) congruence extension property      165—166
Congruence(s), generated by a relation      6
Congruence(s), idempotent-consistent      50 123
Congruence(s), idempotent-determined      108
Congruence(s), idempotent-pure      108
Congruence(s), idempotent-separating      50—53 57 58 61 67 104 108
Congruence(s), idempotent-surjective      50
Congruence(s), identity      7
Congruence(s), intersection of      6
Congruence(s), least band      58
Congruence(s), least group      45 53—54 58 98 99
Congruence(s), least inverse      11 59
Congruence(s), least semilattice      37 55
Congruence(s), left (right)      6
Congruence(s), minimum contained in an equivalence      7
Congruence(s), Rees      7
Congruence(s), trace of      54
Congruence(s), universal      6
Consistent pairing of trees      209—210
Convex subset      95
Core of a semigroup      55 59 124
CYCLE      68
Cyclic conjugate      179
Defect of a mapping      3 230
Derivation diagram      74
Diagram      74
Diagram, group      183
Diagram, group, (source- sink-) reduced      185
Diagram, involutary      178
Diagram, over a semigroup      178
Diagram, R-      181—182
Diagram, semigroup      183
Diagram, short      170—171
Diagram, source-reduced (sink-reduced)      78
Diagram, T-minimal      169—170
Digraph      69
Digraph, complete      69
Digraph, functional      70
Digraph, strong      69
Digraph, weak      70
Digraph, weakly connected      70
Dipath      69
Direct product      2
Directed map      177
Dominate      143
Dominion      143 160 165
Dual      2
Dual directional      80
Dual reflection      80
Dual semigroup      11 80
Edge(s)      68
Edge(s), coinitial (coterminal)      77
Edge(s), negative      69
Edge(s), oriented      69
Edge(s), positive      69
Egg-box diagram      16
Elementary R-transition      7
Endomorphism      2 153
Epimorphically embedded      143
Epimorphism      2 13 143
Equational class      10
Equivalence(s)      5 7
Equivalence(s), classes      5
Equivalence(s), generated by a relation      6
Equivalence(s), intersection of      6
Euler — Mascheroni constant      198
Even-odd offspring      206
Eventual regularity      49—52 67
Factor set      5
Free group      92 178
Free inverse semigroup      10—12 81—97 108
Free monogenic inverse semigroup      81 92
Free product of semigroups      161
Free product with amalgamation      160—161
Free semigroup      9—10 15
Full subset      59
Full transformation semigroup      3 12 29 30 148—149 154 157 166 187—200 204—236
Generalized inverse semigroup      48 57 149—151
Generator(s)      3 10
Generator(s) and relations      9—11
Gluskin’s Lemma      212
Graph      68
Graph, acyclic      68
Graph, centre of      69
Graph, left (right) graph      77—79
Graph, radius of      69
Gravity of a mapping      223 230
Green’s Lemma      17 51 135
Green’s relations      15—16
Green’s relations in a regular $\mathcal{D}$-class      19
Group      3 12
Group, embeddable      14 186
Group, inverse      33
Group, left (right)      13 14
Group, maximal      18
Group, of automorphisms      5
Group, of units      5 31
Group, Schiitzenberger      20—21
Group, symmetric      4
Group-bound semigroup      4 12 21 23—28 36 48
Hasse diagram      24
Homomorphism      2
Homomorphism with involution      15
Ideal (left, right)      3
Ideal (left, right), (0-) minimal      29 37
Ideal (left, right), (left, right) principal      3 67 204
Ideal (left, right), 0-minimal left (right)      35—36
Ideal (left, right), extension      7 141
Ideal (left, right), generated by a set      3
Ideal (left, right), order      98
Idempotent      1
Idempotent, central      39
Idempotent, primitive      33 38 42
Idempotent-separating congruence      50—53 57 58 61
Idempotent-separating congruence, maximum      51—53 57 67
Identity element      1
Identity element, right (left)      2
In-tree (out-tree)      70
In-tree (out-tree), root-directed      71
INDEX      4 73
Inflation of a semigroup      15
INTERFACE      169 183
Inverse (of an element)      4
Inverse (of an element) of a relation      7
Inverse (of an element), Moore — Penrose      4
Inverse (of an element), strong      212
Inverse semigroup      4 151 156—157 165
Inverse semigroup, 0-simple      42
Inverse semigroup, E-unitary      98—107
Inverse semigroup, free      11—12 15 81—97 108
Inverse semigroup, free, monogenic      81 92
Inverse semigroup, strict      107
Inverse semigroup, symmetric      4 30 45 105 154 157
Inverse subsemigroup(s)      104 212 222
Inverse subsemigroup(s), entire      106
Involution      11
Isbell’s Zigzag Theorem      144—158
Isbell’s Zigzag Theorem for commutative semigroups      165
Isomorphism      2
Isomorphism of biordered sets      61 112
Isomorphism of Rees semigroups      37
Isomorphism of word trees      83
Iterative range      192—197
Kernel of a homomorphism      5
Kernel of a mapping      5
Kernel of a semigroup      28
Kernel of an orbit of a mapping      72
Label(s) of a walk      83
Label(s), (left, right) boundary      74
Label(s), group      178
Label(s), semigroup      178
Labelling function      178
Labelling function, involutary      178
Lallement’s Lemma      9 15 50
Lattice of (left, right) congruences      7
Lattice of equivalences      7
Lattice of subalgebras      5
Left (right) cycle      78 183—184
Local submonoid(s)      65
Local submonoid(s), subsemigroup(s)      43
Main permutation      72 73
McAlister triple      97
McAlister’s P-Theorem      103
McAlister’s Second Theorem      106 108
Minimal conditions      23—28
Minimal idempotent generating set      231—236
Monogenic semigroup      3 12
Monoid      1
Monoid, bicyclic      31 36 37 58
Monoid, bisimple      22
Monoid, embedding      22
Monoid, free      10
Monomorphism      2 13
Monomorphism of word trees      83
Natural mapping      5
Nilpotent(s)      36 236
Null semigroup      2 29
Orbit(s) of a mapping      72
Orbit(s) of a mapping, acyclic      223
Orbit(s) of a mapping, cyclic      223 236
Orbit(s) of a mapping, of general type      223
Orbit(s) of a mapping, singleton      223
Orthodox semigroup      9 32 42 58 59
P-semigroup(s)      98—109
P-semigroup(s), equivalent      108—109
Partial order(s)      44—49 79
Partial order(s) on Green’s factor sets      16
Partial order(s), compatibility with multiplication      49 65—66
Partial order(s), left (right) partial order on a semigroup      45—46
Partial order(s), natural, partial order on a regular semigroup      46
Partial order(s), natural, partial order on a semigroup      46—49 57
Partial order(s), natural, partial order on an inverse semigroup      44—45 48
Partial order(s), natural, partial order on idempotents      2 57
Partial transformation(s)      4
Partial transformation(s), semigroup of      4 157 166 212 223
Path      68
Path, $(\alpha,\beta)$      82
Path, $(\alpha,\beta)$, length of      82
Penrose generalized inverse      4
Period      4 73
Periodic semigroup      4 12 ?6
Permutation identity      156 157—158
Piece      168
Pre-inverse      136 139
Pre-order      16 60 218
Presentation      10
Presentation, cycle-free      77 78
Presentation, Finite      10
Presentation, of a monoid      10
Presentation, of a semigroup      10
Presentation, of the free inverse semigroup      10
Presentation, positive      182
Presentation, reduced      176
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