---

＜電子ブック＞
The Theory of Lattice-Ordered Groups / by V.M. Kopytov, N.Ya. Medvedev
(Mathematics and Its Applications ; 307)

版	1st ed. 1994.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1994
本文言語	英語
大きさ	XVI, 400 p : online resource
著者標目	*Kopytov, V.M author Medvedev, N.Ya author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Group theory LCSH:Mathematical logic FREE:Order, Lattices, Ordered Algebraic Structures FREE:Group Theory and Generalizations FREE:Mathematical Logic and Foundations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-94-015-8304-6

 類似資料