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Авторизация |
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Higgins P. — Techniques of Semigroup Theory |
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Предметный указатель |
Preston — Wagner Theorem 8
Principal factor(s) 29 41 91
Quasi-inverse 73
Quasi-order 16
R-word 168
Rank 3 188 235 236
Receiver 70 74 184—185
Rectangular band 2 38 43
Rectangular group 42
Rees congruence 7
Rees matrix semigroup 34 41 42
Rees — Suschkewitsch Theorem 35
Region(s) 74
Region(s), inversely labelled 183 184
Region(s), symmetrically labelled 169
Regular -class 19
Regular element 4
Regular sandwich matrix 35
Regular semigroup 4
Relation, compatibility relation on symmetric inverse semigroup 45 107
Relation, congruence generated by 7
Relation, equivalence 6 7
Relation, identity 7
Relation, inverse of a 7
Relation, Nambooripad 46
Relation, universal 6
Relational product 5
Representation extension property 161 162 164 166
Representation(s) 3 51
Representation(s) of a biordered set 115
Representation(s), (left, right) regular 3
Representation(s), extended (left, right) regular 3 34
Representation(s), Preston — Wagner 9
Representation(s), Scheiblich 92—97 108
Right (left) identity 2
Root of an in-tree 71
Sandwich matrix 34
Sandwich matrix, regular 35
Sandwich set(s) 55 134—141
Sandwich set(s) of a pair of elements 64 66
Sandwich set(s) of a pair of idempotents 55 56 61 112
Sandwich set(s) of an n-tuple of idempotents 136
Sandwich set(s), eventually non-empty 142
Saturated subset (of a congruence) 108
Schein left (right) canonical form 95 108
Semiband 56 59 121 123 135 137 236
Semidirect product 104
Semigroup 1
Semigroup, (0-) bisimple 16 22 36
Semigroup, (left, right) cancellative 3 12 29 79
Semigroup, (left, right) T-nilpotent 158
Semigroup, 0-simple 28 36 42
Semigroup, absolutely closed 143
Semigroup, abundant 31 32
Semigroup, archimedean 43
Semigroup, Baer — Levi 14 27 37 157
Semigroup, Brandt 42 156 165
Semigroup, C(n) 168—176
Semigroup, closed 143 162
Semigroup, commutative 2 43 154
Semigroup, commutative regular 40
Semigroup, completely (0-) simple 33—37 42 66 126 141
Semigroup, completely regular 4 37—41 72 157
Semigroup, completely semisimple 41 59 91 152—153
Semigroup, Croisot — Teissier 28
Semigroup, dense 143
Semigroup, diagram 73—80
Semigroup, dual 11
Semigroup, E-solid 59
Semigroup, E-unitary 59
Semigroup, eventually regular 49—52 59 67 123
Semigroup, finite 0-simple 34
Semigroup, finitely presented 10
Semigroup, free 9—10 15
Semigroup, free inverse 10—12 15 81—97
Semigroup, free monogenic inverse 81 92
Semigroup, full transformation 3 12 29 148—149 154 157 166 187—200 204—236
Semigroup, fundamental 53 123
Semigroup, generalized inverse 48 57 149—151
Semigroup, group-bound 4 12 21 23—38 36 48 59
Semigroup, idempotent-consistent 50 123 124
Semigroup, inflation of a 15
Semigroup, inverse see “Inverse semigroup”
Semigroup, left (right) inner 148
Semigroup, left (right) isolated 148
Semigroup, left (right) reductive 14
Semigroup, left (right) simple 3 12 148
Semigroup, left (right) unipotent 32 67
Semigroup, left (right) zero 2 65 166
Semigroup, locally - (-) unipotent 65 67
Semigroup, locally finite 33
Semigroup, locally inverse 48 57 66
Semigroup, locally orthodox 67
Semigroup, locally regular 43
Semigroup, locally T-semigroup 43 65
Semigroup, M-semigroup 62 67
Semigroup, monogenic 3 12
Semigroup, nilpotent generated 236
Semigroup, nowhere commutative 43
Semigroup, null 2 157
Semigroup, of binary relations 5
Semigroup, of order-preserving mappings 187 200—202 203—204
Semigroup, of singular mappings 223 230—231 233—235
Semigroup, orthodox 9 32 42 58 59 67
Semigroup, P-semigroup 98—109
| Semigroup, partial transformation 4 30 154 157 166 212 223
Semigroup, periodic 4 12
Semigroup, reductive 14
Semigroup, Rees 34 41 42
Semigroup, regular 4
Semigroup, residually finite 91
Semigroup, saturated 143
Semigroup, semisimple 29 43
Semigroup, simple 3 16 30 31
Semigroup, small overlap 168
Semigroup, symmetric inverse see “Inverse semigroup”
Semigroup, weakly cancellative 42
Semilattice 2
Semilattice of completely simple semigroups 38
Semilattice of free inverse semigroup 97
Semilattice of groups 39—40 157
Semilattice of rectangular bands 38
Semilattice, congruence 37—38
Semilattice, inflation of a 15
Semilattice, local 43
Semilattice, lower 2
Singular mappings 223 230—231 233—235
Sink 70 74
Solidity of M(e, f) 129
Source 70 74
Stable range 71 72 192—197
Strong semilattice of abelian groups 39
Strong semilattice of groups 39
Strong semilattice of semigroups 39
Subdiagram 75
Subgroup 4
Subsemigroup 2
Subsemigroup, dense 143
Subsemigroup, full 54
Subsemigroup, generated by a set 3
Subsemigroup, self-conjugate 54
Symmetric group 4
Symmetric inverse semigroup 4 45
Symmetrized subset 179
Tournament 69
Trail 68
Transition 7
Transition, elementary R- 7
Translation (s) (left, right) 3
Translation (s) (left, right), linked 20
Transmitter 70 74 184—185
TREE 68
Tree, centre of a 39 83
Tree, even (odd) 206
Tree, parent 206—209
Tree, word 82
Tree, word, birooted 88—91
Union of groups 3 33 66 157
Unit (left, right) 31
Unitary subset (left, right) 56—57
Universal relation 6
Variety 10
Variety, commutative 155—156
Variety, heterotypical 156
Vertices 68
Vertices, central 69
Vertices, depth of 214
Vertices, distance between 69
Vertices, eccentricity of 69
Vertices, extremal 78
Vertices, grasp of 216
Vertices, height of 214
Vertices, hyperbolic 79
Vertices, level of 216
Vertices, reachable 70
Vertices, superfluous 168
Walk 68
Walk, 82
Walk, (proper) segment of 68
Walk, closed 68
Walk, directed 69
Walk, left (right) 78
Walk, length of a 68 69
Walk, null 68 82
Walk, open 68
Walk, spanning 82
Walk, two-sided 69
Wallis product 201
Word problem for C(3) semigroups 175
Word problem for free inverse semigroup 91
Word problem, one-relator 167 186
Word tree 82
Word tree, birooted 88—91
Word(s), cyclically reduced 179
Word(s), down- (up-) 176
Word(s), freely equal 179
Word(s), literally equal 178
Word(s), positive 178
Word(s), reduced 92
Word(s), shuffle- 176
Word(s), trivial 179
Zero element 1
Zero element, left (right) 2
Zero-divisor 33
Zigzag(s) 144 162 165
Zigzag(s), equivalent 147
Zigzag(s), left-inner (right-inner) 148
Zigzag(s), length of 144
Zigzag(s), spine of 144
Zigzag(s), type I, type II(a), type II(b) 163—164
Zigzag(s), value of 144
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