Finite semigroups and universal algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1994
|
| Schriftenreihe: | Series in algebra
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 511 S. Ill., graph. Darst. |
| ISBN: | 9810218958 |
Internformat
MARC
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| 240 | 1 | 0 | |a Semigroups finitos e álgebra universal |
| 245 | 1 | 0 | |a Finite semigroups and universal algebra |c Jorge Almeida |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1994 | |
| 300 | |a XVI, 511 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Series in algebra |v 3 | |
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Datensatz im Suchindex
| _version_ | 1804127982581710848 |
|---|---|
| adam_text | Table of Contents
Preface vii
0 Introduction 1
0.1 Free semigroups, rational languages 1
0.2 Recognizability by finite automata and by finite
semigroups 3
0.3 Syntactical classification of rational languages? ... 5
0.4 Typical questions involving pseudovarieties 6
1 Finite Universal Algebra 9
1 Elements of Universal Algebra 11
1.1 Algebraic types 11
1.2 Homomorphisms, congruences, subalgebras,
direct products 19
1.3 Free algebras, varieties, identities 24
1.4 Completeness of equational logic 28
2 Order and Topology 33
2.1 Well quasi orderings 33
2.2 Uniform structures 45
2.3 The completion of partially ordered sets 48
3 Finite Algebras 53
3.1 Pseudovarieties; recognizability of subsets
of free algebras 53
3.2 Definition of pseudovarieties by filters of identities . 60
xiii
xiv Table of contents
3.3 Eilenberg type correspondences 65
3.4 Implicit operations and their topological algebra . . 71
3.5 Definition of pseudovarieties by pseudoidentities ... 81
3.6 Topological characterization of recognizability .... 85
3.7 Examples 87
3.8 Closed sets of pseudoidentities 96
4 Decidability 105
4.1 Algorithms 105
4.2 Word problems 107
4.3 Finite bases and decidability 112
II Finite Semigroups and Monoids 121
5 Preliminaries 123
5.1 Green s relations 123
5.2 Some important examples of pseudovarieties 129
5.3 Semigroups of transformations 133
5.4 Combinatorics 135
5.5 Bands 136
5.6 Pointwise properties of implicit operations 140
5.7 Graphs 142
6 Permutativity 149
6.1 Varieties of commutative semigroups 149
6.2 Pseudovarieties of commutative semigroups 160
6.3 Linear identities 167
6.4 Permutative semigroups 175
6.5 Minimal non permutative pseudovarieties 181
7 Operators Relating Semigroups and Monoids 201
7.1 Four natural operators 201
7.2 Some calculations of MV 208
8 Semigroups Whose Regular 2 Classes are
Subsemigroups 215
8.1 Implicit operations on DS 215
Table of contents xv
8.2 Implicit operations on J 224
8.3 Some extensions of J 234
9 The Join 241
9.1 The join G V Com 242
9.2 The join R V L 246
9.3 Join decompositions 254
10 The Semidirect Product 265
10.1 Semidirect product and wreath product 265
10.2 Representation of free objects 272
10.3 Iterated semidirect product of semilattices 278
10.4 Locally trivial pseudovarieties closed
under semidirect product 288
10.5 The Krohn Rhodes decomposition 294
10.6 Semidirect products of the form V * Dfc 299
10.7 The pseudovariety Com * D 311
10.8 The pseudovarieties Comifc * Dn 322
10.9 The pseudovariety J * D 328
10.10 Pseudovarieties closed under semidirect
product 341
11 The Power 357
11.1 Two examples 358
11.2 The operators P and P and their counterparts
for varieties of languages 360
11.3 Identities satisfied by power semigroups 363
11.4 Locally trivial pseudovarieties 368
11.5 Permutative pseudovarieties 371
11.6 Non permutative pseudovarieties 375
11.7 7^ trivial power pseudovarieties 383
11.8 The pseudovariety PJ 395
11.9 Locally commutative power pseudovarieties 404
11.10 Pseudovarieties of aperiodic monoids 412
11.11 Completely regular pseudovarieties 425
xvi Table of contents
12 Factorization of Implicit Operations 429
12.1 Irreducible implicit operations 429
12.2 Chain conditions for principal ideals 433
12.3 An exotic example: QnLSl 436
Open Problems 441
Bibliographic Notes 447
Bibliography 459
Author index 495
Index 501
Notation 507
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:00Z |
| institution | BVB |
| isbn | 9810218958 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009011466 |
| oclc_num | 30733507 |
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| owner | DE-20 DE-83 DE-11 |
| owner_facet | DE-20 DE-83 DE-11 |
| physical | XVI, 511 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in algebra |
| series2 | Series in algebra |
| spelling | Almeida, Jorge Verfasser aut Semigroups finitos e álgebra universal Finite semigroups and universal algebra Jorge Almeida Singapore [u.a.] World Scientific 1994 XVI, 511 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series in algebra 3 Algèbre universelle Algèbre universelle ram Semi-groupes Semigroepen gtt Semigroupes ram Algebra, Universal Semigroups Algebra (DE-588)4001156-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Halbgruppe (DE-588)4022990-7 s Gruppentheorie (DE-588)4072157-7 s Series in algebra 3 (DE-604)BV010096634 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009011466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Almeida, Jorge Finite semigroups and universal algebra Series in algebra Algèbre universelle Algèbre universelle ram Semi-groupes Semigroepen gtt Semigroupes ram Algebra, Universal Semigroups Algebra (DE-588)4001156-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4072157-7 (DE-588)4022990-7 |
| title | Finite semigroups and universal algebra |
| title_alt | Semigroups finitos e álgebra universal |
| title_auth | Finite semigroups and universal algebra |
| title_exact_search | Finite semigroups and universal algebra |
| title_full | Finite semigroups and universal algebra Jorge Almeida |
| title_fullStr | Finite semigroups and universal algebra Jorge Almeida |
| title_full_unstemmed | Finite semigroups and universal algebra Jorge Almeida |
| title_short | Finite semigroups and universal algebra |
| title_sort | finite semigroups and universal algebra |
| topic | Algèbre universelle Algèbre universelle ram Semi-groupes Semigroepen gtt Semigroupes ram Algebra, Universal Semigroups Algebra (DE-588)4001156-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Algèbre universelle Semi-groupes Semigroepen Semigroupes Algebra, Universal Semigroups Algebra Gruppentheorie Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009011466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010096634 |
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