Symmetric inverse semigroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1996
|
| Series: | Mathematical surveys and monographs
46 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 166 S. graph. Darst. |
| ISBN: | 0821806270 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface xiii
Introduction xv
Chapter 1. Decomposing Charts 1
§1 Paths 1
§2 Building Charts from Paths 2
§3 Decomposing Charts into Paths 3
§4 Comments 7
Chapter 2. Basic Observations 9
§5 Idempotents, Nilpotents, Inverses, Conjugacy 9
§6 Index and Period of a Chart 11
§7 Cyclic Subsemigroups of Cn 14
§8 Comments 15
Chapter 3. Commuting Charts 19
§9 Examples 19
§10 Characterization of Commuting Charts 20
§11 Comments 24
Chapter 4. Centralizers of Permutations 25
§12 Examples of Centralizers 25
§13 Centralizers as Directs Products 27
§14 Centralizers and Wreath Products 28
§15 Comments 30
Chapter 5. Centralizers of Charts 33
§16 General Case 33
§17 Nilpotent Case: An Example 34
§18 Nilpotent Case: The Wreath Product 35
§19 The Quotient Semigroup 36
§20 Imbedding C(rj) into the Quotient Semigroup 37
§21 Calculations 40
§22 Orders of Centralizers in Cn 41
§23 Comments 41
ix
x CONTENTS
Chapter 6. Alternating Semigroups 43
§24 Even Charts 43
§25 Members of Acn 44
§26 Generators of Alternating Semigroups 47
§27 Comments 50
Chapter 7. 5n normal Semigroups 53
§28 Examples, Lemma, Overview, Notation 53
§29 X Semigroups 56
§30 Basic Observations 57
§31 Semilattices and Ideals 58
§32 Nonidempotents in 5n normal Semigroups 59
§33 Classification for n 5 62
§34 Classification for n 5 64
§35 Comments 66
Chapter 8. Normal Semigroups and Congruences 69
§36 Examples 69
§37 Congruences on Finite Semilattices 71
§38 Kernels of Congruences 75
§39 Kernels and Normal Semigroups 77
§40 Counting Congruences 80
§41 Comments 81
Chapter 9. Presentations of Symmetric Inverse Semigroups 83
§42 Review: Free Algebras, Presentations, Constructions 83
§43 Technical Lemma 90
§44 Inductive Lemma 94
§45 Comments 96
Chapter 10. Presentations of Alternating Semigroups 97
§46 Defining Relations 97
§47 Acn Technical Lemma 98
§48 Acn Inductive Lemma 102
§49 Comments 105
Chapter 11. Decomposing Partial Transformations 107
§50 Semigroup Hierarchy 107
§51 Path Notation for Partial Transformations 108
§52 Cilia and Cells of Partial Transformations 111
§53 Idempotents and Nilpotents 112
§54 Multiplication of Partial Transformations 112
§55 Cyclic Semigroups of Partial Transformations 114
CONTENTS xi
§56 Comments 115
Chapter 12. Commuting Partial Transformations 117
§57 Examples 117
§58 Mapping Initial Segments and Cells 118
§59 Orders of Centralizers of Idempotents 123
§60 Howie s Theorem 124
§61 Comments 126
Chapter 13. Centralizers, Conjugacy, Reconstruction 129
§62 Centralizers 129
§63 Conjugacy in Cn 130
§64 Conjugacy in PTn 133
§65 Sn normal Semigroups in PTn 133
§66 Graph Reconstruction 133
§67 Isomorphic Categories of Graphs and Semigroup Extensions 136
§68 Semigroup Reconstruction Conjecture 139
§69 Comments 140
Appendix 141
§70 Objects and Elements 141
§71 Groups and Group Morphisms 142
§72 Permutation Groups 143
§73 Centralizers of Permutations as Direct Products 146
§74 Centralizers of Regular Permutations as Wreath Products 147
§75 Semigroups 148
§76 Semigroup Morphisms and Congruences 150
§77 Green s Relations 151
§78 Free Semigroups, Free Monoids, and Free Groups 152
§79 Categories 152
Bibliography 155
Index 163
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| id | DE-604.BV011154539 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:54Z |
| institution | BVB |
| isbn | 0821806270 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007477718 |
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| owner_facet | DE-12 DE-29T DE-188 DE-19 DE-BY-UBM |
| physical | XVIII, 166 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Lipscomb, Stephen 1944- Verfasser (DE-588)1014383781 aut Symmetric inverse semigroups Stephen Lipscomb Providence, RI American Math. Soc. 1996 XVIII, 166 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 46 Inverse Halbgruppe (DE-588)4162222-4 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Inverse Halbgruppe (DE-588)4162222-4 s Symmetrische Gruppe (DE-588)4184204-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1277-7 Mathematical surveys and monographs 46 (DE-604)BV000018014 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007477718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lipscomb, Stephen 1944- Symmetric inverse semigroups Mathematical surveys and monographs Inverse Halbgruppe (DE-588)4162222-4 gnd Symmetrische Gruppe (DE-588)4184204-2 gnd |
| subject_GND | (DE-588)4162222-4 (DE-588)4184204-2 |
| title | Symmetric inverse semigroups |
| title_auth | Symmetric inverse semigroups |
| title_exact_search | Symmetric inverse semigroups |
| title_full | Symmetric inverse semigroups Stephen Lipscomb |
| title_fullStr | Symmetric inverse semigroups Stephen Lipscomb |
| title_full_unstemmed | Symmetric inverse semigroups Stephen Lipscomb |
| title_short | Symmetric inverse semigroups |
| title_sort | symmetric inverse semigroups |
| topic | Inverse Halbgruppe (DE-588)4162222-4 gnd Symmetrische Gruppe (DE-588)4184204-2 gnd |
| topic_facet | Inverse Halbgruppe Symmetrische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007477718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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