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Author : Donald Glen Johnson
Publisher :
ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (276 download)
Download or read book A Structure Theory for a Class of Lattice-ordered Rings written by Donald Glen Johnson and published by . This book was released on 1959 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jingjing Ma
Publisher : World Scientific
ISBN 13 : 981457144X
Total Pages : 258 pages
Book Rating : 4.8/5 (145 download)
Download or read book Lecture Notes On Algebraic Structure Of Lattice-ordered Rings written by Jingjing Ma and published by World Scientific. This book was released on 2014-03-14 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.
Author : Stuart A. Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1441917217
Total Pages : 639 pages
Book Rating : 4.4/5 (419 download)
Download or read book Lattice-ordered Rings and Modules written by Stuart A. Steinberg and published by Springer Science & Business Media. This book was released on 2009-11-19 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules. Steinberg presents the material through 800+ extensive examples of varying levels of difficulty along with numerous exercises at the end of each section. Key topics include: lattice-ordered groups, rings, and fields; archimedean $l$-groups; f-rings and larger varieties of $l$-rings; the category of f-modules; various commutativity results.
Author : M.E Anderson
Publisher : Springer Science & Business Media
ISBN 13 : 9400928718
Total Pages : 197 pages
Book Rating : 4.4/5 (9 download)
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].
Author : W.C. Holland
Publisher : Springer Science & Business Media
ISBN 13 : 9401156409
Total Pages : 334 pages
Book Rating : 4.4/5 (11 download)
Download or read book Ordered Algebraic Structures written by W.C. Holland and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac tivities by the Caribbean Mathematics Foundation (abbr. CMF), which was the principal sponsor of this conference. CMF was inaugurated in 1988 with a conference on Ordered Algebraic Structures. During the years between these two conferences the field has changed sufficiently, both from my point of view and, I believe, that of my co-organizer, W. Charles Holland, to make one wonder about the label "Ordered Algebraic Structures" itself. We recognized this from the start, and right away this conference carried a subtitle, or, if one prefers, an agenda: we concentrated on the one hand, on traditional themes in the theory of ordered groups, including model-theoretic aspects, and, on the other hand, on matters in which topology (more precisely C(X)-style topology) and category theory would play a prominent role. Plainly, ordered algebra has many faces, and it is becoming increas ingly difficult to organize an intimate conference, such as the ones encouraged in the series sponsored by CMF, in this area on a broad set of themes. These proceedings reflect, accurately we think, the spirit of the conferees, but it is not a faithful record of the papers presented at the conference.
Author : Jorge Martínez
Publisher : Springer Science & Business Media
ISBN 13 : 9401117233
Total Pages : 257 pages
Book Rating : 4.4/5 (11 download)
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.
Author : Michael Darnel
Publisher : CRC Press
ISBN 13 : 1000105172
Total Pages : 554 pages
Book Rating : 4.0/5 (1 download)
Download or read book Theory of Lattice-Ordered Groups written by Michael Darnel and published by CRC Press. This book was released on 2021-12-16 with total page 554 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.
Author : A.M. Glass
Publisher : Springer Science & Business Media
ISBN 13 : 9400922833
Total Pages : 398 pages
Book Rating : 4.4/5 (9 download)
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.
Author : V.M. Kopytov
Publisher : Springer Science & Business Media
ISBN 13 : 9401583048
Total Pages : 408 pages
Book Rating : 4.4/5 (15 download)
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.
Author : B. A. Davey
Publisher : Cambridge University Press
ISBN 13 : 9780521784511
Total Pages : 316 pages
Book Rating : 4.7/5 (845 download)
Download or read book Introduction to Lattices and Order written by B. A. Davey and published by Cambridge University Press. This book was released on 2002-04-18 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.
Author : John Edwin Diem
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (828 download)
Download or read book On a Class of Lattice-ordered Rings written by John Edwin Diem and published by . This book was released on with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Laszlo Fuchs
Publisher : Courier Corporation
ISBN 13 : 0486173607
Total Pages : 242 pages
Book Rating : 4.4/5 (861 download)
Download or read book Partially Ordered Algebraic Systems written by Laszlo Fuchs and published by Courier Corporation. This book was released on 2014-03-05 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.
Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 9780821874707
Total Pages : 314 pages
Book Rating : 4.8/5 (747 download)
Download or read book Structure of Rings written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1956-12-31 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karl H. Hofmann
Publisher : Springer
ISBN 13 : 3540370811
Total Pages : 323 pages
Book Rating : 4.5/5 (43 download)
Download or read book Tulane University Ring and Operator Theory Year, 1970-1971 written by Karl H. Hofmann and published by Springer. This book was released on 2006-11-15 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chen-jyi Su
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (353 download)
Download or read book A Structure Theory for Partially Ordered Rings and Algebras written by Chen-jyi Su and published by . This book was released on 1977 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937919
Total Pages : 932 pages
Book Rating : 4.4/5 (899 download)
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.3/5 ( download)
Download or read book Fundamenta Mathematicae written by and published by . This book was released on 1983 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
