Topological Lattice Ordered Groups

Author : M.E Anderson,T.H. Feil
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789400928718

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Lattice-Ordered Groups by M.E Anderson,T.H. Feil Pdf

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].

Author : Robert Lewis Madell
Publisher : Unknown
Page : 204 pages
File Size : 54,7 Mb
Release : 1968
Category : Electronic
ISBN : WISC:89010864965

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Topological Lattice Ordered Groups by Robert Lewis Madell Pdf

Author : Michael Darnel
Publisher : CRC Press
Page : 568 pages
File Size : 49,8 Mb
Release : 2021-12-17
Category : Mathematics
ISBN : 9781000148381

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Theory of Lattice-Ordered Groups by Michael Darnel Pdf

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.

Author : A.M. Glass,W.C. Holland
Publisher : Springer Science & Business Media
Page : 398 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400922839

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Lattice-Ordered Groups by A.M. Glass,W.C. Holland Pdf

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.

Author : V.M. Kopytov,N.Ya. Medvedev
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 53,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401583046

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The Theory of Lattice-Ordered Groups by V.M. Kopytov,N.Ya. Medvedev Pdf

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.

Author : Michael Darnel
Publisher : CRC Press
Page : 554 pages
File Size : 46,8 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781000105179

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Theory of Lattice-Ordered Groups by Michael Darnel Pdf

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.

Author : A.M. Glass,W.C. Holland
Publisher : Springer
Page : 380 pages
File Size : 53,7 Mb
Release : 2011-10-02
Category : Mathematics
ISBN : 9400922841

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Lattice-Ordered Groups by A.M. Glass,W.C. Holland Pdf

Author : Andrew Martin William Glass
Publisher : World Scientific
Page : 326 pages
File Size : 45,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9810234937

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Partially Ordered Groups by Andrew Martin William Glass Pdf

"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

Author : W. B. Powell
Publisher : CRC Press
Page : 220 pages
File Size : 47,7 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 082477342X

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Ordered Algebraic Structures by W. B. Powell Pdf

The papers contained in this volume constitute the proceedings of the Special Session on Ordered Algebraic Structures which was held at the 1982 annual meeting of the American Mathematical Society in Cincinnati, Ohio. The Special Session and this volume honor Paul Conrad, whose work on the subject is noted for its depth and originality. These papers address many areas within the subject of ordered algebraic structures, including varieties, free algebras, lattice ordered groups, subgroups of ordered groups, semigroups, ordered rings, and topological properties of these structures.

Author : Adam Clay,Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 51,9 Mb
Release : 2016-11-16
Category : Knot theory
ISBN : 9781470431068

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Ordered Groups and Topology by Adam Clay,Dale Rolfsen Pdf

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Author : Andrew Martin William Glass
Publisher : Cambridge University Press
Page : 333 pages
File Size : 44,7 Mb
Release : 1981
Category : Mathematics
ISBN : 9780521241908

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Ordered Permutation Groups by Andrew Martin William Glass Pdf

As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.

Author : Paul F. Conrad
Publisher : Unknown
Page : 326 pages
File Size : 54,5 Mb
Release : 1970
Category : Group theory
ISBN : STANFORD:36105033265476

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Lattice Ordered Groups by Paul F. Conrad Pdf

Author : Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 51,9 Mb
Release : 1996-04-30
Category : Mathematics
ISBN : 0306110601

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Right-Ordered Groups by Valeriĭ Matveevich Kopytov,V.M. Kopytov,Nikolai Yakovlevich Medvedev Pdf

The notion of right-ordered groups is fundamental in theories of I-groups, ordered groups, torsion-free groups, and the theory of zero-divisors free rings, as well as in theoretical physics. Right-Ordered Groups is the first book to provide a systematic presentation of right-ordered group theory, describing all known and new results in the field. The volume addresses topics such as right-ordered groups and order permutation groups, the system of convex subgroups of a right-ordered group, and free products of right-ordered groups.

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 42,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599641

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Author : Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall
Publisher : American Mathematical Soc.
Page : 478 pages
File Size : 44,8 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 0821885901

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Valuation Theory and Its Applications by Franz-Viktor Kuhlmann,Salma Kuhlmann,Murray Marshall Pdf

This book is the second of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). It contains the most recent applications of valuation theory to a broad range of mathematical ideas. Valuation theory arose in the early part of the twentieth century in connection with number theory and continues to have many important applications to algebra, geometry, and analysis. The research and survey papers in this volume cover a variety of topics, including Galois theory, the Grunwald-Wang Theorem, algebraic geometry, resolution of singularities, curves over Prufer domains, model theory of valued fields and the Frobenius, Hardy fields, Hensel's Lemma, fixed point theorems, and computations in valued fields. It is suitable for graduate students and research mathematicians interested in algebra, algebraic geometry, number theory, and mathematical logic.