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The Theory of Lattice-Ordered Groups

Author: V M Kopytov; N Ya Medvedev
Publisher: Dordrecht : Springer Netherlands, 1994.
Series: Mathematics and Its Applications, 307.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 book 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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V M Kopytov; N Ya Medvedev
ISBN: 9789401583046 9401583048
OCLC Number: 851378734
Description: 1 online resource (xvi, 400 pages).
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.
Series Title: Mathematics and Its Applications, 307.
Responsibility: by V.M. Kopytov, N. Ya. Medvedev.

Abstract:

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 book 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 excellent introduction to the theory of partially ordered groups, and as an overview of new ideas and results in this theory.

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