Lattice-Ordered Groups: An Introduction

1: Fundamentals.- Section 1: Preliminaries and Basic Examples.- Section 2: Subobjects and Morphisms.- 2: Bernau's representation for Archimedean ?-groups.- 3: The Conrad-Harvey-Holland Representation.- 4: Represent able and Normal-valued ?-groups.- Section 1: The Lorenzen Representation for ?-groups.- Section 2: Normal-valued ?-groups.- 5: Holland's Embedding Theorem.- 6: Free ?-groups.- 7: Varieties of ?-groups.- Section 1: The lattice of Varieties.- Section 2: Covers of the Abelian Variety.- Section 3: The Cardinality of the lattice of ?-group Varieties.- 8: Completions of Representable and Archimedean ?-groups.- Section 1: Completions of Representable ?-groups.- Section 2: Completions of Archimedean ?-groups.- 9: The Lateral Completion.- 10: Finite-valued and Special-valued ?-groups.- 11: Groups of Divisibility.- Appendix: A Menagerie of Examples.- Section 1: Varieties of ?-groups.- Section 2: Torsion and Radical Classes of ?-groups.- Section 3: Examples of Lattice-ordered Groups.- Author Index.