TABLE OF CONTENTS
vii
11.2 Decomposition of an operand; fully reducible operands and
semigroups . . . . . . . .
(Theorem 11.3-Theorem 11.4)
11.3 Strictly cyclic operands and modular right congruences.
(Lemma 11.5-Theorem 11.10)
11.4 Representations by one-to-one partial transformations.
(Corollary 11.11-Corollary 11.15)
11.5 Irreducible and transitive operands and semigroups.
(Lemma 11.16-Theorem 11.22)
11.6 Various radicals of a semigroup . . . . .
(Theorem 11.23-Corollary 11.27)
11.7 The normalizer of a right congruence p and the endomorphisms
of Sip
(Theorem 11.28)
11.8 Representations by monomial matrices
(Theorem 11.29)
11.9 Other types of representations . . . . .
(Lemma 11.30-Lemma 11.32)
256
259
263
269
274
279
280
284
CHAPTER 12. EMBEDDING A SEMIGROUP IN A GROUP
12.1 The free group on a semigroup . . . . .
(Lemma 12.1-Construction 12.3)
12.2 The general problem of embedding a semigroup in a group
(Theorem 12.4-Theorem 12.6)
12.3 Ptak's conditions for embeddability .
(Theorem 12.7-Theorem 12.10)
12.4 The construction of quotients . . . .
(Lemma 12.11-Lemma 12.15)
12.5 Lambek's polyhedral conditions for embeddability
(Theorem 12.16)
12.6 Malcev's conditions for embeddability
(Theorem 12.17-Lemma 12.20)
12.7 Comparison of Malcev and Lambek systems
(Theorem 12.21-Lemma 12.23)
12.8 Finite sets of equational implications .
(Lemma 12.24-Corollary 12.31)
288
292
294
297
303
309
319
323
BIBLIOGRAPHY
ERRATA TO VOLUME I
AUTHOR INDEX .
INDEX
APPENDIX .
334
341
343
345
351
Previous Page Next Page