Preface |
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iii | |
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The Interplay of Algebra and Order |
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1 | (36) |
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1 | (1) |
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Partially Ordered Sets, Directed Sets, and Lattices |
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2 | (4) |
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Partially Ordered Groups and Directed Groups |
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6 | (3) |
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9 | (7) |
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Absolute Values and the Triangle Inequalities |
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16 | (5) |
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l-permutations and l-homomorphisms |
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21 | (5) |
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l-subgroups and Saturated Subgroups |
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26 | (11) |
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37 | (32) |
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Convex Sets and Subgroups |
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37 | (7) |
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l-ideals and the Coset Ordering |
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44 | (4) |
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48 | (5) |
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Regular Subgroups and Values |
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53 | (2) |
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Γ(G) and Plenary Subsets of Γ(G) |
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55 | (6) |
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Convex l-subgroups of l-subgroups |
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61 | (8) |
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Polars and Disjoint Elements |
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69 | (50) |
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70 | (6) |
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Polars and Prime Subgroups |
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76 | (6) |
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82 | (2) |
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Cardinal Sums and Summands |
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84 | (6) |
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Polar Subgroups of l-subgroups |
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90 | (3) |
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Projectable and Strongly Projectable l-groups |
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93 | (4) |
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Convex o-subgroups and Basic Elements |
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97 | (7) |
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104 | (15) |
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119 | (18) |
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Closed Convex l-subgroups |
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120 | (9) |
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Completely Distributive l-groups |
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129 | (4) |
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Essential Subgroups and the Essential Radical |
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133 | (4) |
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Totally Ordered Structures |
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137 | (26) |
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137 | (11) |
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148 | (2) |
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150 | (4) |
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Lex Extensions and Lex Subgroups |
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154 | (9) |
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Order-preserving Permutations of a Chain |
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163 | (52) |
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164 | (5) |
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The Cayley-Holland Theorem |
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169 | (4) |
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Convex l-subgroups of A(Omega;) |
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173 | (4) |
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177 | (7) |
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184 | (9) |
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Primitive l-group Actions and Their Classifications |
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193 | (9) |
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Cardinality Bounds on l-groups |
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202 | (3) |
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205 | (10) |
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215 | (42) |
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216 | (11) |
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227 | (12) |
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A Brief Introduction to l-varieties |
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239 | (10) |
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The Lateral Completion of an l-group |
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249 | (8) |
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257 | (44) |
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257 | (5) |
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The l-variety of Normal-valued l-groups |
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262 | (7) |
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c-groups and Free Normal-valued l-groups |
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269 | (3) |
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Above and Below Subgroups in Normal-valued l-groups |
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272 | (2) |
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Completely Distributive Normal-valued l-groups |
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274 | (1) |
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275 | (19) |
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294 | (7) |
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Representable and Abelian l-groups |
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301 | (58) |
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301 | (8) |
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Completions of Representable l-groups |
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309 | (6) |
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Sheaf-theoretic Representations of Representable l-groups |
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315 | (9) |
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Weakly Abelian and Nilpotent l-groups |
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324 | (9) |
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Abelian l-groups and Vector Lattices |
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333 | (11) |
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Free Abelian l-groups and Vector Lattices |
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344 | (15) |
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359 | (60) |
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General Results on Archimedean l-groups |
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359 | (10) |
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369 | (11) |
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Hyperarchimedean l-groups |
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380 | (8) |
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p-endomorphisms of an Archimedean l-groups |
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388 | (16) |
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Representation by Almost-finite Continuous Functions |
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404 | (15) |
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419 | (54) |
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The l-semigroup of l-varieties |
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419 | (17) |
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Powers of the Representable l-variety |
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436 | (10) |
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l-varieties Based on Finite Conjugate Disjointness |
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446 | (7) |
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453 | (20) |
Appendix One: The (G) Problem |
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473 | (4) |
Appendix Two: Piecewise Linear Homogeneous Representations of Abelian l-groups |
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477 | (10) |
Sources for the Chapters |
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487 | (10) |
Bibliography |
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497 | (32) |
Symbols |
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529 | (2) |
Index |
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531 | |