Willkommen, schön sind Sie da!
Logo Ex Libris

The Theory of Lattice-Ordered Groups

  • Fester Einband
  • 420 Seiten
(0) Erste Bewertung abgeben
Bewertungen
(0)
(0)
(0)
(0)
(0)
Alle Bewertungen ansehen
A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set whic... Weiterlesen
CHF 165.00
Print on demand - Exemplar wird für Sie besorgt.
Bestellung & Lieferung in eine Filiale möglich

Beschreibung

A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathemat ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc tion of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For exam ple, partially ordered groups with interpolation property were intro duced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P.

Inhalt

Preface. Symbol Index. 1. Lattices. 2. Lattice-ordered groups. 3. Convex l-subgroups. 4. Ordered permutation groups. 5. Right-ordered groups. 6. Totally ordedered 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. Bibliography. Index.

Produktinformationen

Titel: The Theory of Lattice-Ordered Groups
Autor:
EAN: 9780792331698
ISBN: 0792331699
Format: Fester Einband
Herausgeber: Springer Netherlands
Anzahl Seiten: 420
Gewicht: 793g
Größe: H241mm x B160mm x T27mm
Jahr: 1994
Auflage: 1994

Weitere Produkte aus der Reihe "Mathematics and Its Applications"