TABLE OF CONTENTS
PREFACE TO VOLUME II . . . . . . . . ix
NOTATION USED IN VOLUME II . . . . . . . xi
CHAPTER 6. MINIMAL IDEALS AND MINIMAL CONDITIONS
6.1
6.2
6.3
6.4
6.5
6.6
0-minimal zero i d e a l s . . . . . . . .
(Lemma 6.1-Theorem 6.9)
The two-sided ideal generated by a 0-minimal right ideal
(Lemma 6.10-Theorem 6.19)
The right socle of a semigroup . . . . . .
(Lemma 6.20-Corollary 6.24)
Combined theory of the left and right socles of a semigroup
(Theorem 6.25-Corollary 6.30)
0-direct unions of 0-simple semigroups . . . . .
(Lemma 6.31-Theorem 6.40)
MR, ML and similar minimal conditions . . . .
(Lemma 6.41-Theorem 6.49)
1
8
12
16
23
30
CHAPTER 7. INVERSE SEMIGROUPS
7.1 The natural partial order on an inverse semigroup
(Lemma 7.1-Theorem 7.5)
7.2 Partial right congruences on an inverse semigroup
(Lemma 7.6-Lemma 7.14)
7.3 Representations by one-to-one partial transformations
(Lemma 7.15-Theorem 7.33)
7.4 Homomorphisms of inverse semigroups
(Lemma 7.34-Theorem 7.48)
7.5 Semilattices of inverse semigroups
(Theorem 7.49-Corollary 7.53)
7.6 Homomorphisms which separate idempotents
(Theorem 7.54-Theorem 7.58)
7.7 Homomorphisms onto primitive inverse semigroups
(Theorem 7.59-Theorem 7.70)
CHAPTER 8. SIMPLE SEMIGROUPS
8.1 Baer-Levi semigroups . . . . . . . 82
(Lemma 8.1-Theorem 8.8)
8.2 Croisot-Teissier semigroups. . . . . . . 86
(Lemma 8.9-Theorem 8.19)
42
47
57
64
65
71
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