Preface |
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ix | |
Introduction |
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1 | (4) |
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Lattices, Semigroups, and Varieties |
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5 | (52) |
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6 | (1) |
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7 | (6) |
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Lattice of Equivalence Relations |
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13 | (3) |
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16 | (4) |
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Homomorphisms and Congruences |
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20 | (8) |
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28 | (5) |
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33 | (4) |
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37 | (7) |
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44 | (4) |
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48 | (9) |
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57 | (55) |
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57 | (6) |
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Variety of Completely Regular Semigroups |
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63 | (5) |
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68 | (5) |
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73 | (10) |
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83 | (5) |
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88 | (4) |
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92 | (5) |
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97 | (5) |
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Representation by Transformations |
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102 | (10) |
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Completely Simple Semigroups |
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112 | (50) |
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113 | (4) |
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117 | (7) |
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Homomorphisms Between Rees Matrix Semigroups |
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124 | (8) |
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Congruences on a Rees Matrix Semigroup |
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132 | (10) |
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142 | (7) |
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Commutativity Properties of the Structure Group |
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149 | (6) |
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Translational Hull of a Rees Matrix Semigroup |
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155 | (7) |
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162 | (41) |
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163 | (8) |
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171 | (8) |
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***-Majorization and ***-Minorization |
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179 | (8) |
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Special Classes of Orthogroups |
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187 | (4) |
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Quasivarieties of Normal Bands |
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191 | (6) |
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Join of Quasivarieties of Normal Bands |
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197 | (6) |
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203 | (40) |
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All Varieties of Regular Bands |
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203 | (7) |
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210 | (8) |
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218 | (3) |
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221 | (5) |
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Regular Orthocryptogroups |
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226 | (6) |
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A Lattice of Regular Orthogroup Varieties |
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232 | (5) |
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Minimal Noncryptic Varieties |
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237 | (6) |
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243 | (40) |
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244 | (9) |
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253 | (5) |
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258 | (5) |
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263 | (6) |
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Congruences and Green's Relations |
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269 | (8) |
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Congruences Induced by Green's Relations |
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277 | (6) |
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Relations on the Congruence Lattice |
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283 | (60) |
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284 | (6) |
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290 | (7) |
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Kernels of Orthodox Congruences |
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297 | (8) |
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Left Mark and Left Kernel Relations |
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305 | (9) |
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314 | (4) |
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318 | (4) |
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322 | (6) |
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328 | (5) |
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Construction of Congruences |
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333 | (4) |
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Congruences on Normal Cryptogroups |
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337 | (6) |
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Varieties of Completely Simple Semigroups |
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343 | (54) |
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Varieties of Rectangular Groups |
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344 | (4) |
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Free Completely Simple Semigroups |
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348 | (5) |
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Fully Invariant Congruences |
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353 | (5) |
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358 | (4) |
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Varieties *** and ***H*** |
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362 | (3) |
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Varieties ***, C***, and *** |
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365 | (12) |
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A Homomorphism of the Lattice *** |
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377 | (6) |
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Varieites of Central Completely Simple Semigroups |
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383 | (4) |
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All Varieties of Overabelian Completely Simple Semigroups |
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387 | (4) |
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Finitely Generated Free Completely Simple Semigroups |
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391 | (6) |
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Malcev Product and Homomorphisms |
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397 | (45) |
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Malcev Product of Varieties |
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398 | (4) |
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Malcev Products *** where *** |
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402 | (5) |
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407 | (4) |
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Malcev Products of *** and with *** |
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411 | (4) |
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Malcev Products of *** with *** and *** |
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415 | (5) |
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420 | (4) |
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424 | (3) |
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Homomorphisms Induced by Monoids |
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427 | (7) |
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Endomorphisms Induced by *** and *** |
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434 | (8) |
Bibliography |
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442 | (19) |
Index of Symbols |
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461 | (12) |
Author Index |
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473 | (4) |
Subject Index |
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477 | |