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Petrich M. — Inverse semigroups
Petrich M. — Inverse semigroups



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Название: Inverse semigroups

Автор: Petrich M.

Аннотация:

In its half-century history, the theory of semigroups has grown from modest attempts to generalize both group theory and ring theory in the direction of a single binary operation obeying only the associative law to the present stage of an independent branch of algebra with a large body of important results.
The first books on semigroup theory represented attempts to systematize most of the knowledge on the subject, whereas later works have tended to cover only some particular areas. One of the areas of semigroup theory which showed great popularity almost from its beginning is that of inverse semigroups. The present book represents the first attempt to systematize the principal parts of the theory of inverse semigroups. Not all results in this area are included, but the main subjects are treated in complete detail from elementary definitions to the frontier of the existing state of the art.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 680

Добавлена в каталог: 29.10.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E$-reflexive inverse semigroup      157
$E$-unitary cover      326
$E$-unitary cover, $S$ has $E$-unitary covers (over $\mathcal{U}$)      559
$E$-unitary cover, $\mathcal{V}$ has $E$-unitary covers (over $\mathcal{U}$)      559
$E$-unitary cover, cover for $S$ over a group      323
$E$-unitary cover, inverse semigroup      151
$F$-inverse cover for $M$ over $G$      353
$F$-inverse cover for $M$ over $G$, semigroup      340
$F$-pair      347
$P$-extension      250
$P$-extension, $p$-ideal      7
$P$-extension, $po$-group      451
$P$-representation      312
$P$-semigroup      312
$R$-inverse semigroup      335
0-bisimple semigroup      27
0-direct union      14
0-simple semigroup      24
0-sub transitive semigroup      174
0-subuniform semilattice      174
0-transitive semigroup      174
0-uniform semilattice      174
Abelian group part      545
Adjacent vertices      370
Adjoin an identity      12
Alphabet      51
Amalgam in $\mathcal{C}$      62
Amalgam in $\mathcal{C}$ of semigroups $S_{i}$, with core $U$      61
Amalgamated free product      67
Antiautomorphism      18
Antigroup      134
Antiisomorphism of lattices      6
Antiisomorphism of lattices of semigroups      17
Antiuniform semilattice      175
Associative law      12
Automorphism      17
Band      13
Basis      386
Basis for the identities in a variety      55
Basis, $T$-basis      386
Basis, property      386
Bicyclic semigroup      113
Biideal      241
Birkhoffs theorem      55
Birooted word tree      371
Bisimple semigroup      27
Bitranslation      38
Brandt groupoid      611
Brandt groupoid, representation      95
Brandt groupoid, semigroup      92
Bruck semigroup (over a monoid)      106
Bruck semigroup (over a monoid), over a monoid $T$ with endomorphism a      106
C-morphism      73
C-object      73
Cancellative semigroup      41
Canonical homomorphism of $S$ into $\Psi(K)$      247
Canonical homomorphism of $S$ into $\Psi(K)$, homomorphism of $S$ into $\Omega(S)$      39
Canonical homomorphism of $S$ into $\Psi(K)$, homomorphism of $V$ into $\Omega(S)$      43
Canonical homomorphism of $S$ into $\Psi(K)$, order of idempotents      14
Canonical homomorphism of $S$ into $\Psi(K)$, partial order      79
Categorical at zero      25
Categorical at zero, ideal      25
Category      73
Center      14
centralizer      14
Chain      6
Chain of groups      507
Chain of semigroups      83
Chain, $\omega$-chain      109
Clifford congruence      147
Clifford congruence, representation      86
Clifford congruence, semigroup      85
Clifford congruence, variety      531
Closed path      370
Closed path, subset      79
Closure      79
Combinatorial semigroup      363
Combinatorial semigroup, variety      519
Commutative semigroup      14
Commutator      539
Commuting elements      13
Compatibility relation      129
Compatible elements      129
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$)      277
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), $\bigvee$-homomorphism      8
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), $\bigvee$-sublattice      7
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), $\bigwedge$ -homomorphism      8
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), $\bigwedge$-sublattice      7
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), homomorphism      8
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), lattice      7
Complete class of solutions for the triple ($Ê$, $\pi$,$Q$), sublattice      7
Completely prime ideal      25
Completely prime ideal semisimple variety      548
Completely prime ideal semisimple variety, 0-simple semigroup      25
Completely prime ideal semisimple variety, simple semigroup      25
Completely prime ideal, reflective subset      163
Completely prime ideal, regular element      34
Completely prime ideal, regular semigroup      34
Completely prime ideal, semisimple cryptic variety      548
Completely prime ideal, semisimple semigroup      32
Complex multiplication      12
Complex multiplication, product      212
Component of a groupoid      613
Composition of morphisms      74
Concatenation      51
Congruence      18
Congruence, $\mathcal{C}$-congruence      19
Congruence, congruence      48
Congruence, extension property      588
Congruence, free semigroup      177
Congruence, on a lattice      8
Congruence, pair      118
Conjugate extension      246
Conjugate extension, hull      241
Connected graph      370
Connecting homomorphism      505
Content of a set      366
Content of a set of a word      365
Covered by      7
covers      7
Croisot congruence      137
Croisot congruence, groupoid      611
Cryptic semigroup      548
Cryptic semigroup, variety      548
CYCLE      370
Cyclic semigroup      13
Cyclic semigroup, $\mathcal{D}$-class      27
Defining identities      55
Dense embedding      49
Dense embedding, ideal extension      48
Densely embedded ideal      48
Depth function      389
Direct product      21
Disjunctive subset      137
Distributive lattice      7
Domain      15
Domain of $\tau_{H’}$      183
Domain, $\mathcal{D}$-simple semigroup      27
EDGE      369
Edge, $E$-disjunctive inverse semigroup      140
Effective representation      184
Effective subset      183
Elementary p-transition      20
Embedding      17
Empty relation      8
Empty relation, transformation      15
Empty relation, word      51
Endomorphism      17
Endomorphism, endomorphism      44
Epimorphism      17
Equality relation      8
Equivalence of categories      75
Equivalent categories      76
Equivalent categories, ideal extensions      44
Equivalent categories, normal extensions      276
Equivalent categories, representations      187
Equivalent categories, sets of identities      55
Essential ideal      7
Essential ideal, $P$-extension      250
Extension      42
Extension of $\rho$ to $S$      571
Extension, determined by parameters      233
Extension, determined by partial homomorphism      47
Extension, function      44 230
Extension, problem      42 276
Extension, triple      276
Extreme vertex      370
Faithful representation      18 169
Filter      150 459
Filter, filter      459
Finite chain of groups      501
Finite chain of groups, index      410
Finite chain of groups, index of a variety      544
Finite chain of groups, order      13
Finitely related semigroup      430
Forgetful functor      76
Free Brandt semigroup      99
Free Brandt semigroup, $F$-representation      341
Free Brandt semigroup, $\mathcal{V}$-free product      593
Free Brandt semigroup, algebra      50
Free Brandt semigroup, extension of p to      5 566
Free Brandt semigroup, free algebra      51
Free Brandt semigroup, generators for an inverse semigroup      377
Free Brandt semigroup, group      53
Free Brandt semigroup, inverse semigroup      362
Free Brandt semigroup, object in $\mathcal{C}$ (on $X$)      51
Free Brandt semigroup, product      66
Free Brandt semigroup, product of semigroups $S_{1}$ amalgamating $U$      67
Free Brandt semigroup, product of the amalgam      67
Free Brandt semigroup, representation extension property      569
Free Brandt semigroup, semilattice over P      366
Full closure      243
Full closure, function      89 323
Full closure, functor      75
Full closure, subcategory      74
Full closure, subset      118
Full closure, transformation      16
Fully closed subset      244
Fully closed subset, invariant congruence      57
functor      74
Fundamental inverse semigroup      134
General associative law      12
Generated by      13
Generates S’ (as a monoid)      13
Generators for an inverse semigroup      81
Graph      369
Green’s equivalence      27
Green’s equivalence, lemma      29
Green’s equivalence, relation      27
Group-congruence-free      292
Group-congruence-free of units      12
Group-congruence-free, acts by order automorphisms      302
Group-congruence-free, free product      593
Group-congruence-free, kernel normal system      135
Group-congruence-free, part      526
Groupoid      11
Groupoid, $\mathcal{H}$-class      27
Heterotypical identity      54
Homomorphic image      17
Homomorphism      17
Homomorphism of a lattice      8
Homomorphism, $S$-homomorphism      44
Homotypical identity      54
Ideal      23
Ideal of a partially ordered set      7
Ideal, extension      42
Idealizer      25
Idempotent      13 612
Idempotent, determined congruence      136
Idempotent, metacenter      247
Idempotent, pure congruence      136
Idempotent, separating congruence      131
Identical relation      8
Identity      12 54
Identity, functor      75
Identity, mapping      16
Identity, morphism      74
Identity, valid in a variety      55
Implication      60
Imprint      628
Index of a variety      544
Induced by      254
Induces a congruence      19
Inductive groupoid      626
Infinite index      410
Infinite index, order      13
Initial segment      490
Inner automorphism induced by      17
Inner automorphism induced by, bitranslation induced by      38
Inner automorphism induced by, left translation induced by      38
Inner automorphism induced by, part of $\Omega($S$), $\Lambda($S$), P($S$)      38
Inner automorphism induced by, part of $\Psi$($S$)      247
Inner automorphism induced by, right translation induced by      38
interval      7
Intraregular semigroup      511
Inverse      35
Inverse of a binary relation      9
Inverse of a morphism      74
Inverse of a subset      212
Inverse of an element      35
Inverse, free product      593
Inverse, hull      439
Inverse, relation      9
Inverse, semigroup      78
Inverse, subsemigroup generated by      81
Inverse, triple      617
Invertible element      12
Inverts order      6
Involution      18
Irredundant subset      386
Irredundant subset, $T$-irredundant      386
Isomorphic objects      74
Isomorphism      17 74
Isomorphism of lattices      8
Isomorphism of word trees      370
Isomorphism, $S$-isomorphism      44
Isomorphism, $\mathcal{J}$-class      27
Join      6
Joined by an edge      370
Joined by an edge, $\mathcal{J}$-structure mapping      631
Juxtaposition      51
Kernel class      139
Kernel class of a congruence      117
Kernel class of a semigroup      25
Kernel class, in a semigroup      137
Kernel class, normal system      120
Labeled edge      370
Lallement’s Lemma      36
Lattice      6
Lattice, ordered group      451
Law in a semigroup      54
Law in a semigroup, in a variety      55
Layer      389
Layered semigroup      389
Layered semigroup, $\mathcal{L}$-class      27
Left cancellative semigroup      41
Left cancellative semigroup, congruence      18
Left cancellative semigroup, ideal      23
Left cancellative semigroup, identity      12 612
Left cancellative semigroup, normal divisor      465
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