Download or read book The Theory of Lattice Ordered Groups written by V.M. Kopytov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lattice Ordered Groups written by A.M. Glass and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lattice Ordered Groups written by M.E Anderson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Download or read book Theory of Lattice Ordered Groups written by Michael Darnel and published by CRC Press. This book was released on 2021-12-17 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partially Ordered Groups written by Andrew Martin William Glass and published by World Scientific. This book was released on 1999 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Universal Algebra and Lattice Theory written by R.S. Freese and published by Springer. This book was released on 2006-11-15 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordered Groups and Infinite Permutation Groups written by W.C. Holland and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.
Download or read book Ordered Algebraic Structures written by W. B. Powell and published by CRC Press. This book was released on 1985-10-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Orders Description and Roles written by M. Pouzet and published by Elsevier. This book was released on 1984-01-01 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orders: Description and Roles
Download or read book Ordered Algebraic Structures written by Jorge Martínez and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the 1991 Conrad Conference, held in Gainesville, Florida, USA, in December, 1991. Together, these give an overview of some recent advances in the area of ordered algebraic structures. The first part of the book is devoted to ordered permutation groups and universal, as well as model-theoretic, aspects. The second part deals with material variously connected to general topology and functional analysis. Collectively, the contents of the book demonstrate the wide applicability of order-theoretic methods, and how ordered algebraic structures have connections with many research disciplines. For researchers and graduate students whose work involves ordered algebraic structures.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1981-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005-06 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1981-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1999 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1972-12 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Global Subdirect Products written by Peter H. Krauss and published by American Mathematical Soc.. This book was released on 1979 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: An internal characterization is given of those subdirect products which are structures of global sections of discrete sheaves. Such subdirect products are called global. Patching of subdirect products over a dual ring of subsets of the index set is defined, and a uniform method of constructing global subdirect products from the patching property is developed. The role of the hull-kernel topology in sheaf constructions is analyzed in the setting of universal algebra. Global subdirect products which come from Hausdorff sheaves over Boolean spaces (Boolean subdirect products) are treated in terms of the normal transform. Global representation of varieties is defined and investigated. Finally, applications to the sheaf representation of rings and lattice ordered rings are a given.
