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Completely Regular Semigroups [Kietas viršelis]

(Simon Fraser University, Burnaby, BC, Canada), (Simon Fraser University, Burnaby, BC, Canada)
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Offers a treatment of completely regular semigroups. Text is written in the manner of complete proofs, except when the relevant statements belong to other branches of algebra. Coverage includes completely simple semigroups, normal cryptogroups, congruences, and Malcev product and homomorphisms. Each chapter ends with exercises designed to either improve the understanding of the material in the section or to extend it. Written as a reference, but can be used in the classroom for a graduate-level course on special topics in algebra, assuming a prerequisite course in semigroup theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.

Recenzijos

"...a thorough and readable account..." (Bulletin of LondonMathematical Society, Vol 32, 2000)

"A large portion of this book is devoted to such special classes ofcompletely regular semigroups: completely simple semigroups, normalcryptogroups an regular othogroups the lattice of congruences of acompletely regular semigroup..." (Zentralblatt MATH, Vol. 967,2001/17)

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


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