Overview

This volume makes both classical and new results of the theory of lattice-ordered groups available to a wide range of mathematicians in a comprehensive way, explaining the structure of the theory as well as indicating its applications. The text contains the foundations of the theory of lattice-ordered groups, and the theory of ordered permutation groups. It describes totally-ordered and right-ordered groups, and highlights the theory of varieties and quasi-varieties of lattice-ordered groups. The distinguishing feature of this work is the group-theoretical and universal algebra attitude to the theory of lattice-ordered groups. This volume will be of interest to graduate students and researchers with a basic knowledge of group theory. It serves as an introduction to the theory of partially ordered groups, and as an overview of new ideas and results in this theory.

Full Product Details

Author:   V.M. Kopytov ,  N.Ya. Medvedev
Publisher:   Springer
Imprint:   Springer
Edition:   1994 ed.
Volume:   307
Dimensions:   Width: 15.60cm , Height: 2.30cm , Length: 23.40cm
Weight:   1.690kg
ISBN:  

9780792331698

ISBN 10:   0792331699
Pages:   400
Publication Date:   31 October 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Lattices.- 2 Lattice-ordered groups.- 3 Convex l-subgroups.- 4 Ordered permutation groups.- 5 Right-ordered groups.- 6 Totally ordered groups.- 7 Embeddings of lattice-ordered groups.- 8 Lattice properties in lattice-ordered groups.- 9 Varieties of lattice-ordered groups.- 10 Free l-groups.- 11 The semigroup of l-varieties.- 12 The lattice of l-varieties.- 13 Ordered permutation groups and l-varieties.- 14 Quasivarieties of lattice-ordered groups.

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