Completely Regular Semigroups

Present a systematic treatment of completely regular semigroups, from introductory to research level, comprised of preliminaries on lattices, semigroups, varieties, and complete regularity; congruences and relations on the congruence lattice; and varieties of completely regular semigroups through kernals, and traces of congruences and Malcev products.

Mario Petrich and Norman R. Reilly are the authors of Completely Regular Semigroups, published by Wiley.

Preface

ix

Introduction

1

(4)

Lattices, Semigroups, and Varieties

5

(52)

Notation

6

(1)

Lattices

7

(6)

Lattice of Equivalence Relations

13

(3)

Semigroups

16

(4)

Homomorphisms and Congruences

20

(8)

Ideals and Extensions

28

(5)

Green's Relations

33

(4)

Varieties

37

(7)

Invariants

44

(4)

Free Unary Semigroups

48

(9)

Complete Regularity

57

(55)

Global Structure

57

(6)

Variety of Completely Regular Semigroups

63

(5)

Elementary Properties

68

(5)

Natural Partial Order

73

(10)

Orthogroups

83

(5)

Core

88

(4)

Operators H, L, and C

92

(5)

Cryptogroups

97

(5)

Representation by Transformations

102

(10)

Completely Simple Semigroups

112

(50)

Characterizations

113

(4)

Rees Theorem

117

(7)

Homomorphisms Between Rees Matrix Semigroups

124

(8)

Congruences on a Rees Matrix Semigroup

132

(10)

Rectangular Groups

142

(7)

Commutativity Properties of the Structure Group

149

(6)

Translational Hull of a Rees Matrix Semigroup

155

(7)

Normal Cryptogroups

162

(41)

Characterizations

163

(8)

Normal Orthogroups

171

(8)

***-Majorization and ***-Minorization

179

(8)

Special Classes of Orthogroups

187

(4)

Quasivarieties of Normal Bands

191

(6)

Join of Quasivarieties of Normal Bands

197

(6)

Regular Orthogroups

203

(40)

All Varieties of Regular Bands

203

(7)

Yamada Theorem

210

(8)

Regular Orthogroups

218

(3)

Regular Cryptogroups

221

(5)

Regular Orthocryptogroups

226

(6)

A Lattice of Regular Orthogroup Varieties

232

(5)

Minimal Noncryptic Varieties

237

(6)

Congruences

243

(40)

Kernel

244

(9)

Trace

253

(5)

Congruence Pair

258

(5)

Left Mark and Left Trace

263

(6)

Congruences and Green's Relations

269

(8)

Congruences Induced by Green's Relations

277

(6)

Relations on the Congruence Lattice

283

(60)

Kernel Relation

284

(6)

Trace Relation

290

(7)

Kernels of Orthodox Congruences

297

(8)

Left Mark and Left Kernel Relations

305

(9)

Conguence Networks

314

(4)

Local Relation

318

(4)

Global Relation

322

(6)

***-Related Congruences

328

(5)

Construction of Congruences

333

(4)

Congruences on Normal Cryptogroups

337

(6)

Varieties of Completely Simple Semigroups

343

(54)

Varieties of Rectangular Groups

344

(4)

Free Completely Simple Semigroups

348

(5)

Fully Invariant Congruences

353

(5)

***-Invariant Subgroups

358

(4)

Varieties *** and ***H***

362

(3)

Varieties ***, C***, and ***

365

(12)

A Homomorphism of the Lattice ***

377

(6)

Varieites of Central Completely Simple Semigroups

383

(4)

All Varieties of Overabelian Completely Simple Semigroups

387

(4)

Finitely Generated Free Completely Simple Semigroups

391

(6)

Malcev Product and Homomorphisms

397

(45)

Malcev Product of Varieties

398

(4)

Malcev Products *** where ***

402

(5)

Malcev Products in ***

407

(4)

Malcev Products of *** and with ***

411

(4)

Malcev Products of *** with *** and ***

415

(5)

Relational Morphisms

420

(4)

Preimage Classes

424

(3)

Homomorphisms Induced by Monoids

427

(7)

Endomorphisms Induced by *** and ***

434

(8)

Bibliography

442

(19)

Index of Symbols

461

(12)

Author Index

473

(4)

Subject Index

477

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Completely Regular Semigroups

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

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5% off 1 book, 7% off 2 books, 10% off 3+ books

Completely Regular Semigroups

Summary

Author Biography

Table of Contents

Supplemental Materials

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