Lattice Ordered Groups
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Lattice Ordered Groups
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Author : M.E Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Ordered Groups written by M.E Anderson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Lattice Ordered Groups
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Author : Paul F. Conrad
language : en
Publisher:
Release Date : 1970
Lattice Ordered Groups written by Paul F. Conrad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Group theory categories.
Lattice Ordered Groups
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Author : A.M. Glass
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Ordered Groups written by A.M. Glass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A lattice-ordered group is a mathematical structure combining a (partial) order (lattice) structure and a group structure (on a set) in a compatible way. Thus it is a composite structure, or, a set carrying two or more simple structures in a compatible way. The field of lattice-ordered groups turn up on a wide range of mathematical fields ranging from functional analysis to universal algebra. These papers address various aspects of the field, with wide applicability for interested researchers.
The Lattices Of Subgroups And Varieties Of Lattice Ordered Groups
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Author : Mary Elizabeth Huss
language : en
Publisher:
Release Date : 1981
The Lattices Of Subgroups And Varieties Of Lattice Ordered Groups written by Mary Elizabeth Huss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Group theory categories.
Partially Ordered Groups
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Author : Andrew Martin William Glass
language : en
Publisher: World Scientific
Release Date : 1999
Partially Ordered Groups written by Andrew Martin William Glass and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
"The author's style of writing is very lucid, and the material presented is self-contained. It is an excellent reference text for a graduate course in this area, as well as a source of material for individual reading".Bulletin of London Mathematical Society
The Theory Of Lattice Ordered Groups
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Author : V.M. Kopytov
language : en
Publisher: Springer
Release Date : 2013-01-07
The Theory Of Lattice Ordered Groups written by V.M. Kopytov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-07 with Mathematics categories.
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.
Theory Of Lattice Ordered Groups
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Author : Michael Darnel
language : en
Publisher: CRC Press
Release Date : 2021-12-17
Theory Of Lattice Ordered Groups written by Michael Darnel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Mathematics categories.
Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
Lattice Ordered Groups
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Author : A.M. Glass
language : en
Publisher: Springer
Release Date : 2011-10-02
Lattice Ordered Groups written by A.M. Glass and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-02 with Mathematics categories.
Theory Of Lattice Ordered Groups
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Author : Michael Darnel
language : en
Publisher: CRC Press
Release Date : 2021-12-16
Theory Of Lattice Ordered Groups written by Michael Darnel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
The Theory Of Lattice Ordered Groups
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Author : V.M. Kopytov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Theory Of Lattice Ordered Groups written by V.M. Kopytov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.