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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.

Аннотация:

This book introduces recently developed ideas and techniques in semigroup theory, providing a handy reference guide previously unavailable in a single volume. The opening chapter provides sufficient background to enable the reader to follow any of the subsequent chapters, and would by itself be suitable for a first course in semigroup theory. The second chapter gives an account of free inverse semigroups leading to proofs of the McAlister P-theorems. Subsequent chapters have the underlying theme of diagrams and mappings, and the new material includes the theory of biordered sets of Nambooripad and Easdown, the semigroup diagrams of Remmers and Jackson with applications to the one-relator, and other word problems, a short proof of Isbell's Zigzag theorem with applications to epimorphisms and amalgams, together with combinatorial, probabilistic and graphical techniques used to prove results including Schein's Covering Theorem and Howie's Gravity Formula for finite full transformation semigroups. Nearly two hundred exercises serve the dual purpose of illustrating the richness of the subject while allowing the reader to come to grips with the material.


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
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 $\mathcal{D}$-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 $\mathcal{L}$- ($\mathcal{D}$-) 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, $(\alpha,\beta)-$      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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