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Howie J.M. (ed.) — An Introduction to Semigroup Theory
Howie J.M. (ed.) — An Introduction to Semigroup Theory

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Название: An Introduction to Semigroup Theory

Автор: Howie J.M. (ed.)

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 272

Добавлена в каталог: 18.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr{D}$ (Green's equivalence)      39
$\mathscr{H}$ (Green’s equivalence)      39
$\mathscr{J}$ (Green’s equivalence)      39
$\mathscr{L}$ (Green’s equivalence)      38
$\mathscr{R}$ (Green’s equivalence)      38
$\omega$-semigroup      152
(0-) simple semigroup      57
(left, right) normal band      116 119
(left, right) translation      98 232
(left, right) unitary subset      55
(O-) bisimple semigroup      63
(right) $\omega$-coset      172
(right) coset (of an inverse subsemigroup)      172
(right, left) S-system      223
(S, T)-bisystem      223
0-direct union      71
Absolutely closed semigroup      228
Admissible triple      75
Almost unitary subsemigroup      232
Amalgam      212 217
Amalgam, free inverse product of      246
Amalgam, free product of      217
Amalgam, inverse semigroup      243
Amalgamation property, special      249
Amalgamation property, strong      250
Amalgamation property, weak      220 250
Anti-representation      194
Anti-uniform band      204
Anti-uniform semilattice      144 146
Associated mappings      232 255
Associative      1
atom      114
Automorphism      5
Band      90 95
Band, (left, right) normal      116 119
Band, (left, right) zero      3 119
Band, anti-uniform      204
Band, free      104
Band, rectangular      3 96 119
Band, trivial      119
Band, uniform      203
Bicyclic semigroup      144
Bijection      6
Binary relation(s)      14
Binary relation(s), semigroup of      14
Bruck — Reilly extension      153
Central izer      183
Chain of groups      163
Clifford semigroup      93 163
Closed subsemigroup      220
Closed subset      139
Closure      138 220
Codomain      5
Comparable      148
Completely (0-) simple semigroup      57 60 68
Congruence (s)      21
Congruence (s), fully invariant      110
Congruence (s), generated by a relation      24
Congruence (s), group      139 185
Congruence (s), idempotent-separating      52 140 141
Congruence (s), identical      14
Congruence (s), intersection of      24
Congruence (s), inverse semigroup      190
Congruence (s), join of      27 28
Congruence (s), left (right)      21
Congruence (s), proper      73
Congruence (s), Rees      31
Congruence (s), semilattice      93
Congruence (s), universal      14
Congruence-free semigroup      83
Consistent subsemigroup      254
Content      104 105
Converse (of a relation)      15
Coproduct      217 244
Core      217
Cyclic group      9
Decreasing step      231
Denning relations      30
Dense subsemigroup      220
Diagonal      116
Direct product      5 6 116
Domain (of a mapping)      5
Domain (of a mapping) of a binary relation      15
Dominate      220
Dominion      220
E-unitary, inverse semigroup      181 182
E-unitary, regular semigroup      55 125
Eggbox diagram      42
Elementary R-transition      26
Endomorphism      5
Equality relation      14
Equivalence(s)      18
Equivalence(s) classes      19
Equivalence(s) commuting      29 31
Equivalence(s) compatible      21
Equivalence(s) generated by a relation      19
Equivalence(s) idempotent-separating      52
Equivalence(s) identical      14
Equivalence(s) intersection of      19
Equivalence(s) left (right) compatible      21
Equivalence(s) universal      14
Equivalence(s), join of      27 28
Extension      16
extract      74
Finitely presented semigroup      30
Formal inverse      244
Free band      104
Free inverse product      244
Free inverse semigroup      129
Free product of amalgam      217
Free product of semigroups      212
Free semigroup      29
Full transformation semigroup      6
Generators      7 30
Greatest lower bound      12
Green’s equivalences      38 39
Green’s equivalences in an inverse semigroup      131
Green’s equivalencesin a regular semigroup      49 50
Green’s Lemmas      43
Green’s Theorem      44
Group      4
Group congruence      139
Group left (right)      54
Group minimum congruence      139
Group, 0-      4
Group, symmetric      6
Groupoid      1
Hall semigroup      199
Hall — Yamada semigroup      207
Hasse diagram      14
Homorphism      5
Homorphism Rees      31
Ideal (left, right, two-sided)      5
Ideal, (0-) minimal      58
Ideal, minimum      59
Ideal, principal      38
Ideal, proper      5
Idempotent      5
Idempotent, central      93
Idempotent, primitive      68
Idempotent-separating congruence      52 140 141
Idempotent-separating congruence, maximum      52 141 192
Identical relation      109
Identity element      1
Identity element, left (right)      35
Incomparable      148
Increasing step      230
Index (of an element in a free product)      212
Index (of an element of finite order)      8
Initial      106
Initial, mark      106
Internalized sequence      235
Internalized sequence, fully      235
Internalized sequence, left (right)      235
Inverse of an element      45
Inverse semigroup      129
Inverse semigroup, bisimple      150
Inverse semigroup, free      129
Inverse semigroup, fundamental      141
Inverse semigroup, minimum congruence      190
Inverse semigroup, simple      159
Inverse semigroup, symmetric      134
Inverse subsemigroup      139
Inverse subsemigroup, closed      139
Inverse subsemigroup, full      145
Inverse subsemigroup, normal      181
Inverse subsemigroup, subtransitive      160
Inverse subsemigroup, transitive      151
Irregular $\mathscr{D}$-class      45
Isbell’s Zigzag Theorem      228
Isomorphic      5
Isomorphism      5
Join      12
Kernel of a homomorphism      22 31
Kernel of a mapping      19
Kernel of a semigroup      9 59
Lallement’s Lemma      52
Lattice(s)      12
Lattice(s), complete      12
Lattice(s), direct product of      34
Lattice(s), modular      32
Lattice(s), semimodular      33
Least upper bound      12
Lexicographic order      149
Maximal      12
Maximum      12
Meet      12
Minimal      11
Minimal conditions $min_L$, $min_R$, $min_J$      12 41
Minimum      11
Modular lattice      32
Monogenic semigroup      8
Monoid      2
Monomorphism      5
Morphism (of S-systems)      224
Multiplication      1
Munn semigroup      143
Null semigroup      3
Order of a semigroup      1
Order of an element      8
Order relation      11
Order relation, partial      11
Order relation, total      11
Ordered set      11
Ordered set, partially      11
Ordered set, totally      11
Ordered set, well-      12 147
Ordinal product      184
Orthodox semigroup      186
P-semigroup      182
Partial mapping(s)      16
Partial mapping(s), semigroup of      16
Partition      18
Period      8
Periodic semigroup      11 40
Primitive idempotent      68
Principal (left, right, two-sided) ideal      38
Principal factor      60
Principal series      86
Proper inverse semigroup      see under E-unitary
Pushout      218 246
Quotient semigroup      21 22
Quotient set      19
Range (of a mapping)      5
Range of a binary relation      15
Rectangular band      3 96 119
Rees congruence      31
Rees homomorphism      31
Rees matrix semigroup      62 68
Rees’s Theorem      63
Regular $\mathscr{D}$-class      45
Regular element      44
Regular sandwich matrix      60 62
Regular semigroup      44
Relation      14
Relation, antisymmetric      11
Relation, binary      14
Relation, compatible      21
Relation, congruence      21
Relation, congruence generated by      24
Relation, converse of      15
Relation, equality      14
Relation, equivalence      18
Relation, equivalence generated by      19
Relation, identical      109
Relation, left (right) compatible      21
Relation, order      11
Relation, reflexive      11 18
Relation, symmetric      18
Relation, transitive      11 18
Relation, transitive closure of      19
Relation, universal      14
Representation(s) (by mappings)      6 135 168
Representation(s) extended right regular      7
Representation(s), decomposable      176
Representation(s), effective      169
Representation(s), equivalent      170
Representation(s), faithful      6 168
Representation(s), sum of      170
Representation(s), transitive      169
Representation(s), Vagner — Preston      135 168
Restriction      16
Sandwich matrix      62
Semigroup      1
Semigroup with identity      1
Semigroup with zero      2
Semigroup, (0-) bisimple      63
Semigroup, (right, left) cancellative      53 54
Semigroup, absolutely closed      228
Semigroup, archimedean      125
Semigroup, bicyclic      144
Semigroup, Clifford      93 163
Semigroup, commutative      1
Semigroup, completely (0-) simple      57 60 68
Semigroup, congruence-free      83
Semigroup, finite      11
Semigroup, finitely presented      30
Semigroup, free      29
Semigroup, inverse      129
Semigroup, left (right) simple      54
Semigroup, left (right) zero      3
Semigroup, monogenic      8
Semigroup, null      3
Semigroup, orthodox      186
Semigroup, periodic      11
Semigroup, relatively free      112
Semilattice      14
Semilattice of semigroups      89
Semilattice, anti-uniform      144 146
Semilattice, complete lower      12
Semilattice, complete upper      12
Semilattice, congruence      93
Semilattice, lower      12
Semilattice, minimum congruence      93
Semilattice, subuniform      160
Semilattice, uniform      144 146
Semilattice, upper      12
Semimodular lattice      33
Semisimple      86
Semisimple, (0-) simple      57
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