Theory of Lattice-Ordered Groups

by Michael Darnel

Overview

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.

Product Details

ISBN-13:	9781000148381
Publisher:	CRC Press
Publication date:	12/16/2021
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	560
File size:	943 KB

About the Author

Michael Darnel

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.

Editorial Reviews

A reference for research mathematicians and a text for graduate students who want to become familiar with the standard theorems, constructions, and techniques of lattice-group theory. Assumes a knowledge of free groups, solvable and nilpotent groups, filters, and other topics encountered in graduate courses in group theory and topology. Begins with the general concepts common to all lattice-groups then proceeds through successively finer classes. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"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

From the Publisher