## Semigroups: An Introduction to the Structure TheoryThis work offers concise coverage of the structure theory of semigroups. It examines constructions and descriptions of semigroups and emphasizes finite, commutative, regular and inverse semigroups. Many structure theorems on regular and commutative semigroups are introduced.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc. |

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### Contents

Semigroups | 1 |

Associativity and products | 3 |

Homomorphisms | 9 |

Congruences | 14 |

Free semigroups | 17 |

Presentations | 21 |

Greens Relations | 26 |

Inverses | 32 |

Iterated Rhodes expansions | 175 |

The regular embedding | 178 |

The Synthesis Theorem | 187 |

Regular semigroups | 193 |

The Petrich representation | 198 |

Strict regular semigroups | 200 |

The translational hull of a completely 0simple semigroup | 206 |

Clifford semigroups | 211 |

Schützenberger groups | 38 |

Completely 0simple semigroups | 44 |

The ReesSushkevich Theorem | 51 |

Constructions | 59 |

Semilattice decompositions | 68 |

Subdirect products | 78 |

Group coextensions | 81 |

Commutative semigroups | 94 |

Semigroups of fractions | 95 |

Archimedean decomposition | 98 |

Nsemigroups | 100 |

Archimedean semigroups | 104 |

Ponizovsky decompositions | 109 |

Group coextensions | 114 |

Free commutative semigroups | 121 |

Finite commutative nilsemigroups | 127 |

Finitely generated commutative semigroups | 132 |

The Completion Theorem | 137 |

Finite semigroups | 143 |

Greens relations and homomorphisms | 144 |

Minimal congruences | 146 |

Wreath products and divisibility | 151 |

The KrohnRhodes Theorem | 156 |

Finiteness | 161 |

Rhodes expansions | 167 |

Constructions by triples | 215 |

Inverse semigroups | 226 |

Fundamental inverse semigroups | 230 |

Bisimple wsemigroups | 233 |

Bisimple inverse semigroups | 238 |

Unitary covers | 245 |

The PTheorem | 250 |

Free inverse semigroups | 254 |

Division categories | 267 |

Fundamental regular semigroups | 276 |

Cross connections | 285 |

Biordered sets | 290 |

The fundamental semigroup of a biordered set | 299 |

Structure mappings | 307 |

The fundamental fourspiral semigroup | 315 |

Four classes of regular semigroups | 328 |

Orthodox semigroups | 341 |

Pseudoinverse semigroups | 348 |

Eunitary regular semigroups | 358 |

Szendreis PTheorem | 363 |

Notation | 373 |

375 | |

387 | |

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### Common terms and phrases

0-simple semigroup action archimedean associative Assume band bicyclic bijection biordered set called Chapter Clifford commutative semigroup completely simple congruence consists construction contains Conversely Corollary cross defined definition denote determined direct disjoint Dually E E(S E-unitary element equality Exercises exists factor Finally finite follows functor fundamental given group coextension Hence holds homomorphism ideal ideal extension idempotent identity element implies induces injective integer inverse semigroup isomorphism L-class left ideal Lemma length mapping maximal minimal monoid multiplication nonempty nonzero normal form operation orthodox particular preserving principal projection PROOF properties Proposition Prove Rees matrix regular semigroup representation restriction S)reg satisfies semi semilattice Show Similarly smallest structure subgroup subsemigroup subset subword surjective Theorem Theory trivial union unique universal Verify written yields

### References to this book

Coxeter Groups and Hopf Algebras Marcelo Aguiar,Swapneel Mahajan,Swapneel Arvind Mahajan No preview available - 2006 |