Completely regular semigroups:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1999
|
| Series: | Canadian Mathematical Society series of monographs and advanced texts
23 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 481 S. |
| ISBN: | 0471195715 |
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MARC
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| 245 | 1 | 0 | |a Completely regular semigroups |c Mario Petrich; Norman R. Reilly |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface x
Introduction 1
Chapter 1 Lattices, Semigroups, and Varieties 5
1.1 Notation 6
1.2 Lattices 7
1.3 Lattice of Equivalence Relations 13
1.4 Semigroups 16
1.5 Homomorphisms and Congruences 20
1.6 Ideals and Extensions 28
1.7 Green s Relations 33
1.8 Varieties 37
1.9 Invariants 44
1.10 Free Unary Semigroups 48
Chapter 2 Complete Regularity 57
II. 1. Global Structure 57
11.2 Variety of Completely Regular Semigroups 63
11.3 Elementary Properties 68
11.4 Natural Partial Order 73
11.5 Orthogroups 83
11.6 Core 88
11.7 Operators H, L, and C 92
11.8 Cryptogroups 97
11.9 Representation by Transformations 102
Chapter 3 Completely Simple Semigroups 112
111.1 Characterizations 113
111.2 Rees Theorem 117
111.3 Homomorphisms Between Rees Matrix
Semigroups 124
V
vi Contents
111.4 Congruences on a Rees Matrix Semigroup 132
111.5 Rectangular Groups 142
111.6 Commutativity Properties of the Structure Group 149
111.7 Translational Hull of a Rees Matrix Semigroup 155
Chapter 4 Normal Cryptogroups 162
IV. 1 Characterizations 163
IV.2 Normal Orthogroups 171
IV.3 ^-Majorization and ^-Minorization 179
IV.4 Special Classes of Orthogroups 187
IV.5 Quasivarieties of Normal Bands 191
IV.6 Join of Quasivarieties of Normal Bands 197
Chapter 5 Regular Orthogroups 203
V.I All Varieties of Regular Bands 203
V.2 Yamada Theorem 210
V.3 Regular Orthogroups 218
V.4 Regular Cryptogroups 221
V.5 Regular Orthocryptogroups 226
V.6 A Lattice of Regular Orthogroup Varieties 232
V.7 Minimal Noncryptic Varieties 237
Chapter 6 Congruences 243
VI. 1 Kernel 244
VI.2 Trace 253
VI.3 Congruence Pair 258
VI.4 Left Mark and Left Trace 263
VI.5 Congruences and Green s Relations 269
VI.6 Congruences Induced by Green s Relations 277
Chapter 7 Relations on the Congruence Lattice 283
VII. 1 Kernel Relation 284
VII.2 Trace Relation 290
VII.3 Kernels of Orthodox Congruences 297
VII.4 Left Mark and Left Kernel Relations 305
VII.5 Congruence Networks 314
VII.6 Local Relation 318
VII.7 Global Relation 322
VII.8 ^-Related Congruences 328
VII.9 Construction of Congruences 333
VII.10 Congruences on Normal Cryptogroups 337
Contents vii
Chapter 8 Varieties of Completely Simple Semigroups 343
VIII.1 Varieties of Rectangular Groups 344
VIII.2 Free Completely Simple Semigroups 348
VIII.3 Fully Invariant Congruences 353
VIII.4 ^-Invariant Subgroups 358
VIII.5 Varieties Tn^ and ^Wr 362
VIII.6 Varieties (Jf), CV, and tTv S 365
VIII.7 A Homomorphism of the Lattice £ e fCHs4) 377
VIII.8 Varieties of Central Completely Simple
Semigroups 383
VIII.9 All Varieties of Overabelian Completely Simple
Semigroups 387
VIII.10 Finitely Generated Free Completely Simple
Semigroups 391
Chapter 9 Malcev Product and Homomorphisms 397
IX. 1 Malcev Product of Varieties 398
IX.2 Malcev Products % ° f where W e ££((9) 402
IX.3 Malcev Products in £ ( $Sf) 407
IX.4 Malcev Products of Si, S, m S, and M$ with -r 411
IX.5 Malcev Products of M^ with £%, if, £J,r%,
and i£8l@ 415
IX.6 Relational Morphisms 420
IX.7 Preimage Classes 424
IX.8 Homomorphisms Induced by Monoids 427
IX.9 Endomorphisms Induced by ^, ^ Sf, £%, M3£,
and M® 434
Bibliography 442
Index of Symbols 461
Author Index 473
Subject Index 477
|
| any_adam_object | 1 |
| author | Petrich, Mario Reilly, Norman R. |
| author_GND | (DE-588)139925953 |
| author_facet | Petrich, Mario Reilly, Norman R. |
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| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T22:24:53Z |
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| isbn | 0471195715 |
| language | English |
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| physical | X, 481 S. |
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| series2 | Canadian Mathematical Society series of monographs and advanced texts |
| spelling | Petrich, Mario Verfasser aut Completely regular semigroups Mario Petrich; Norman R. Reilly New York [u.a.] Wiley 1999 X, 481 S. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society series of monographs and advanced texts 23 Reilly, Norman R. Verfasser (DE-588)139925953 aut Canadian Mathematical Society Canadian Mathematical Society series of monographs and advanced texts 23 (DE-604)BV012067942 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642904&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrich, Mario Reilly, Norman R. Completely regular semigroups |
| title | Completely regular semigroups |
| title_auth | Completely regular semigroups |
| title_exact_search | Completely regular semigroups |
| title_full | Completely regular semigroups Mario Petrich; Norman R. Reilly |
| title_fullStr | Completely regular semigroups Mario Petrich; Norman R. Reilly |
| title_full_unstemmed | Completely regular semigroups Mario Petrich; Norman R. Reilly |
| title_short | Completely regular semigroups |
| title_sort | completely regular semigroups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642904&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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