Semigroups:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | Undetermined |
| Published: |
Providence, RI
Providence, RI
1974
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| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| ISBN: | 0821815539 |
Staff View
MARC
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Chapter I. The concept of a semigroup 1
1. Multiplicative sets 1
2. Independence of the conditions of associativity 11
3. General semigroups and semigroups of transformations 15
4. Partial transformations 28
5. Relations 33
Chapter II. Divisibility of elements 43
1. Concept and elementary properties of divisibility 43
2. Inverse elements and units 47
3. Divisibility of transformations and matrices 53
4. Commutative semigroups of idempotents 56
5. Semigroups in which every element has a right zero 65
6. Regular elements 71
7. Inverse semigroups 78
8. Inverse semigroups of partial transformations 85
Chapter III. Multiplications of subsets 91
1. Subsemigroups 91
2. Generating sets 98
3. Monogenic semigroups 106
4. Periodic semigroups 113
5. Magnifying elements 118
6. Magnifying elements in semigroups with unit 121
7. The subsemigroup characteristic of a semigroup 127
Chapter IV. Ideals 138
1. The concept of ideals and their simplest properties 138
2. Chains of subsets of an arbitrary set 145
3. Principal ideals and ideal layers 150
4. Two sided ideal chains 157
5. The interrelations of ideal equivalences 165
6. Isolated ideals 172
Chapter V. Semigroups with minimal ideals 179
1. Two sided ideals that are groups 179
2. Semigroups with minimal left ideals 182
3. Semigroups with both minimal left ideals and minimal right ideals . . . 189
4. Completely simple semigroups with zero 194
5. The structure of completely simple semigroups with zero 201
6. The structure of completely simple semigroups without zero 210
7. Minimal ideals of semigroups of transformations 217
8. Semigroups of endomorphisms 222
xi
xii CONTENTS
Chapter VI. Invertibility 226
1. Invertibility of the product of elements 226
2. Invertibility of magnifying elements 234
3. Semigroups with one sided invertibility 237
4. Subsemigroups regular with respect to invertibility 245
5. Semigroups of transformations regular with respect to invertibility . . . 248
6. Groups with separating group part 256
7. Subsemigroups of a semigroup with separating group part 260
Chapter VII. Homomorphisms 264
1. Homomorphisms and their divisibility 264
2. Factor semigroups 273
3. Homomorphisms of inverse semigroups 278
4. Normal complexes 284
5. Extension of homomorphisms 295
6. Certain special kinds of homomorphisms 301
Chapter VIII. Decomposition of semigroups into unions of subsemigroups . . 315
1. Bands of semigroups 315
2. Completely regular semigroups 322
3. Completely regular inverse semigroups 329
4. Successively annihilating bands 338
5. Basis classes 344
Chapter IX. Relations in semigroups 353
1. Denning systems of relations 353
2. Transformations of defining systems of relations 358
3. Semigroups given by defining relations 362
4. Identities in semigroups 367
5. Free semigroups 372
6. Determination of free semigroups by the subsemigroup characteristic . . 382
Chapter X. Embedding of semigroups 391
1. Some cases of embedding 391
2. Embedding in groups 396
3. Linear ordering in groups 402
4. Potential invertibility of elements 411
5. Free and direct products 418
6. Representations of semigroups by partial transformations 424
7. Translations of semigroups 428
Chapter XI. Subdirect products 435
1. The notion of subdirect product 435
2. Subdirectly indecomposable semigroups 438
3. Restrictive semigroups 442
4. Weakly cancellative semigroups 446
5. Approximation properties 452
Chapter XII. Identities 457
1. The operators e and n 457
2. The relation of consequential!ty between identities 462
CONTENTS xiii
3. Irreducible families of identities 462
4. Varieties of semigroups 471
5. The lattice of varieties of semigroups 477
6. Identical inclusions 485
Bibliography 489
Supplementary Bibliography (1968) 511
Supplementary Bibliography (1972) 513
Index 517
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| author_facet | Ljapin, E. S. |
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| author_sort | Ljapin, E. S. |
| author_variant | e s l es esl |
| building | Verbundindex |
| bvnumber | BV013488953 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)252348235 (DE-599)BVBBV013488953 |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:43Z |
| institution | BVB |
| isbn | 0821815539 |
| language | Undetermined |
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| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Providence, RI |
| record_format | marc |
| spelling | Ljapin, E. S. Verfasser aut Semigroups 3. ed. Providence, RI Providence, RI 1974 txt rdacontent n rdamedia nc rdacarrier Halbgruppe (DE-588)4022990-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009205950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ljapin, E. S. Semigroups Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4022990-7 |
| title | Semigroups |
| title_auth | Semigroups |
| title_exact_search | Semigroups |
| title_full | Semigroups |
| title_fullStr | Semigroups |
| title_full_unstemmed | Semigroups |
| title_short | Semigroups |
| title_sort | semigroups |
| topic | Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009205950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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