A Study Of Partially Ordered Ring
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Partially Ordered Algebraic Systems
Author | : Laszlo Fuchs |
Publisher | : Courier Corporation |
Total Pages | : 242 |
Release | : 2014-03-05 |
Genre | : Mathematics |
ISBN | : 0486173607 |
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.
A study of partially-ordered rings
Author | : Huei-Jan Shyr |
Publisher | : |
Total Pages | : 202 |
Release | : 1971 |
Genre | : Rings (Algebra) |
ISBN | : |
Partially Ordered Rings and Semi-Algebraic Geometry
Author | : Gregory W. Brumfiel |
Publisher | : Cambridge University Press |
Total Pages | : 293 |
Release | : 1979-12-20 |
Genre | : Mathematics |
ISBN | : 052122845X |
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.
Nearrings, Nearfields And Related Topics
Author | : Kuncham Syam Prasad |
Publisher | : World Scientific |
Total Pages | : 324 |
Release | : 2016-11-28 |
Genre | : Mathematics |
ISBN | : 981320737X |
Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G
Abelian Groups and Representations of Finite Partially Ordered Sets
Author | : David Arnold |
Publisher | : Springer Science & Business Media |
Total Pages | : 256 |
Release | : 2012-11-14 |
Genre | : Mathematics |
ISBN | : 1441987509 |
The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.
Lattice-ordered Rings and Modules
Author | : Stuart A. Steinberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 639 |
Release | : 2009-11-19 |
Genre | : Mathematics |
ISBN | : 1441917217 |
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.
Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings
Author | : Niels Schwartz |
Publisher | : Springer |
Total Pages | : 276 |
Release | : 2006-11-13 |
Genre | : Mathematics |
ISBN | : 3540482849 |
The book lays algebraic foundations for real geometry through a systematic investigation of partially ordered rings of semi-algebraic functions. Real spectra serve as primary geometric objects, the maps between them are determined by rings of functions associated with the spectra. The many different possible choices for these rings of functions are studied via reflections of partially ordered rings. Readers should feel comfortable using basic algebraic and categorical concepts. As motivational background some familiarity with real geometry will be helpful. The book aims at researchers and graduate students with an interest in real algebra and geometry, ordered algebraic structures, topology and rings of continuous functions.
Lecture Notes On Algebraic Structure Of Lattice-ordered Rings
Author | : Jingjing Ma |
Publisher | : World Scientific |
Total Pages | : 258 |
Release | : 2014-03-14 |
Genre | : Mathematics |
ISBN | : 981457144X |
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.
The Spectrum of a Ring as a Partially Ordered Set
Author | : William James Lewis |
Publisher | : |
Total Pages | : 78 |
Release | : 1971 |
Genre | : Rings (Algebra). |
ISBN | : |