1st Edition

Theory of Lattice-Ordered Groups

By Michael Darnel Copyright 1994

    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.

    The interplay of algebra and order

    Convex lattice-ordered subgroups

    Polars and disjoint element

    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

    Biography

    Michael Darnel

    "The author. . .carries the reader to the frontiers of current research. . . . . .a useful reference. "
    ---Mathematical Reviews
    ". . .includes detailedproofs of the theorems and all the material needed from partially ordered setsand lattices. "
    ---Analele Stiintifice
    ". . .an up-to-date and systematic treatment of many topics in the theory of lattice-ordered groups. "
    ---Acta Scientifica Matematica