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The Theory of Lattice-Ordered Groups (Paperback, Softcover reprint of hardcover 1st ed. 1994)
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The Theory of Lattice-Ordered Groups (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Series: Mathematics and Its Applications, 307
Expected to ship within 10 - 15 working days
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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."
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