Semigroups: An Introduction to the Structure Theory

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CRC Press, Aug 8, 1995 - Mathematics - 408 pages
This 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
Bibliography and References
375
Index
387
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About the author (1995)

P. A. Grillet is a Professor of Mathematics at Tulane University, New Orleans, Louisiana.

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