vi TABLE OF CONTENTS
2.4 The Schutzenberger group of an ^-class . . . . 63
(Lemma 2.21-Theorem 2.25)
2.5 0-minimal ideals and 0-simple semigroups . . . . 66
(Lemma 2.26-Theorem 2.35)
2.6 Principal factors of a semigroup . . . . . . 7 1
(Theorem 2.36-Corollary 2.42)
2.7 Completely 0-simple semigroups . . . . . . 76
(Lemma 2.43-Corollary 2.56)
CHAPTER 3. REPRESENTATION BY MATRICES OVER A GROUP WITH ZERO
3.1 Matrix semigroups over a group with zero . . . .
(Lemma 3.1-Theorem 3.3)
3.2 The Rees Theorem
(Theorem 3.4-Lemma 3.6)
3.3 Brandt groupoids . . . . . . . .
(Lemma 3.7-Theorem 3.9)
3.4 Homomorphisms of a regular Rees matrix semigroup
(Lemma 3.10-Theorem 3.14)
3.5 The Schutzenberger representations . . . . .
(Lemma 3.15-Theorem 3.17)
3.6 A faithful representation of a regular semigroup .
(Lemma 3.18-Theorem 3.21)
CHAPTER 4. DECOMPOSITIONS AND EXTENSIONS
4.1 Croisot's theory of decompositions of a semigroup .
(Lemma 4.1-Theorem 4.4)
4.2 Semigroups which are unions of groups . . . .
(Theorem 4.5-Theorem 4.11)
4.3 Decomposition of a commutative semigroup into its archi-
medean components; separative semigroups
(Theorem 4.12-Theorem 4.18)
4.4 Extensions of semigroups . . . . . . .
(Theorem 4.19-Theorem 4.21)
4.5 Extensions of a group by a completely 0-simple semigroup;
equivalence of extensions . . . . . .
(Theorem 4.22-Theorem 4.24)
CHAPTER 5. REPRESENTATION BY MATRICES OVER A FIELD
5.1 Representations of semisimple algebras of finite order . . 1 4 9
(Lemma 5.1-Theorem 5.11)
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