Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
Table of Contents
The interplay of algebra and order; convex lattice-ordered subgroups; polars and disjoint elements; complete distibutivity; totally ordered structures; order preserving permutations of a chain; classes of lattice-ordered groups; normal-valued lattice-ordered groups; representable and abelian lattice-ordered groups; Archimedian lattice-ordered groups; lattice-ordered varieties.
"The author. . .carries the reader to the frontiers of current research. . . . . .a useful reference. "
". . .includes detailedproofs of the theorems and all the material needed from partially ordered setsand lattices. "
". . .an up-to-date and systematic treatment of many topics in the theory of lattice-ordered groups. "
---Acta Scientifica Matematica