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