Rings Of Ordered Field Valued Continuous Functions

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Rings of Ordered Field Valued Continuous Functions

Author : S.K. Acharyya
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Rings of Ordered Field Valued Continuous Functions by : S.K. Acharyya

Download or read book Rings of Ordered Field Valued Continuous Functions written by S.K. Acharyya and published by . This book was released on 2018 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this paper is to investigate the role of the real field in the theory of Rings of Continuous Functions. In the process the real field has been replaced by an ordered field equipped with its order topology and the function rings of continuous functions on topological spaces are investigated. Apart from generalising the classical theorems of M. H. Stone, Gelfand and Kolmogorov, we have obtained nontrivial generalisations for the classical Banach-Stone Theorem -- our version really does not depend on the range of the continuous functions but only depend on the domain topological space. We have also characterised the class of all locally compact non-compact zero dimensional topological spaces as well as the class of all nowhere locally compact zero dimensional spaces using the subrings of functions with compact support. This part of the investigation is carried further to the effect that we have achieved to obtain a kind of Banach-Stone's Theorem for the locally compact non-compact zero dimensional topological spaces using this function ring. The main achievement of this paper is to classify the collection of all zero dimensional but not strongly zero dimensional topological spaces into three kinds, labeled by three inequalities of three compactifications of such spaces.

Rings of Continuous Functions with Values in an Archimedean Ordered Field

Author : Giuseppe De_Marco
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Rings of Continuous Functions with Values in an Archimedean Ordered Field by : Giuseppe De_Marco

Download or read book Rings of Continuous Functions with Values in an Archimedean Ordered Field written by Giuseppe De_Marco and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rings of Continuous Functions with Values in a Non-archimedean Ordered Field

Author : Giuseppe De_Marco
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Rings of Continuous Functions with Values in a Non-archimedean Ordered Field by : Giuseppe De_Marco

Download or read book Rings of Continuous Functions with Values in a Non-archimedean Ordered Field written by Giuseppe De_Marco and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rings of Continuous Functions

Author : L. Gillman
Publisher : Springer Science & Business Media
ISBN 13 : 1461578191
Total Pages : 307 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Rings of Continuous Functions by : L. Gillman

Download or read book Rings of Continuous Functions written by L. Gillman and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to those who know the meaning of each word in the title: none is defined in the text. The reader can estimate the knowledge required by looking at Chapter 0; he should not be dis couraged, however, if he finds some of its material unfamiliar or the presentation rather hurried. Our objective is a systematic study of the ring C(X) of all real-valued continuous functions on an arbitrary topological space X. We are con cerned with algebraic properties of C(X) and its subring C*(X) of bounded functions and with the interplay between these properties and the topology of the space X on which the functions are defined. Major emphasis is placed on the study of ideals, especially maximal ideals, and on their associated residue class rings. Problems of extending continuous functions from a subspace to the entire space arise as a necessary adjunct to this study and are dealt with in considerable detail. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5 and the beginning of Chapter 10, presents the fundamental aspects of the subject insofar as they can be discussed without introducing the Stone-Cech compactification. In Chapter 3, the study is reduced to the case of completely regular spaces.

Ordered Algebraic Structures

Author : W.C. Holland
Publisher : Springer Science & Business Media
ISBN 13 : 9401156409
Total Pages : 334 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Ordered Algebraic Structures by : W.C. Holland

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.

Rings of Continuous Function

Author : Aull
Publisher : CRC Press
ISBN 13 : 9780824771447
Total Pages : 342 pages
Book Rating : 4.7/5 (714 download)

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Book Synopsis Rings of Continuous Function by : Aull

Download or read book Rings of Continuous Function written by Aull and published by CRC Press. This book was released on 1985-03-27 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely work is the first book in several years to review and update important developments in the study of rings of continuous functions. Integrating the recent efforts of leading mathematicians, Rings of Continuous Functions presents chapters with varying emphasis on algebra, analysis, and general topology with particular focus on category theory, cardinality axioms, and set theory. Additionally, historical perspectives and a review of early contributions by leading Soviet mathematicians such as P. S. Aleksandrov and A. N. Tychonov help provide a full, up-to-date understanding of current knowledge. An unparalleled overview of the state of the art, Rings of Continuous Functions will be an invaluable reference for topologists, algebraists, analysts, and geometers active in the field, and an excellent introduction for interested nonspecialist mathematicians. Also, research problems raised in each chapter and in a special final chapter offer provocative avenues for further research -- facilitated by more than 300 literature citations. Book jacket.

Ordered Algebraic Structures

Author : Jorge Martínez
Publisher : Springer Science & Business Media
ISBN 13 : 9400924720
Total Pages : 288 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Ordered Algebraic Structures by : Jorge Martínez

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 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Caribbean Mathematics Foundation Conference, held in Curaçao, August 1988

Entire Functions and Related Parts of Analysis

Author : Jacob Korevaar
Publisher : American Mathematical Soc.
ISBN 13 : 0821814117
Total Pages : 562 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Entire Functions and Related Parts of Analysis by : Jacob Korevaar

Download or read book Entire Functions and Related Parts of Analysis written by Jacob Korevaar and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Quadratic Forms over Fields

Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quadratic Forms over Fields by : Tsit-Yuen Lam

Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

Partially Ordered Algebraic Systems

Author : Laszlo Fuchs
Publisher : Courier Corporation
ISBN 13 : 0486173607
Total Pages : 242 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Partially Ordered Algebraic Systems by : Laszlo Fuchs

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.

Real Algebraic Geometry and Ordered Structures

Author : Charles N. Delzell
Publisher : American Mathematical Soc.
ISBN 13 : 0821808044
Total Pages : 320 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Real Algebraic Geometry and Ordered Structures by : Charles N. Delzell

Download or read book Real Algebraic Geometry and Ordered Structures written by Charles N. Delzell and published by American Mathematical Soc.. This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.

Super-real Fields

Author : Harold G. Dales
Publisher : Oxford University Press
ISBN 13 : 9780198539919
Total Pages : 378 pages
Book Rating : 4.5/5 (399 download)

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Book Synopsis Super-real Fields by : Harold G. Dales

Download or read book Super-real Fields written by Harold G. Dales and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.

Lattice-ordered Rings and Modules

Author : Stuart A. Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1441917217
Total Pages : 639 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Lattice-ordered Rings and Modules by : Stuart A. Steinberg

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.

Spaces of Orderings and Abstract Real Spectra

Author : Murray A. Marshall
Publisher : Springer
ISBN 13 : 3540699961
Total Pages : 191 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Spaces of Orderings and Abstract Real Spectra by : Murray A. Marshall

Download or read book Spaces of Orderings and Abstract Real Spectra written by Murray A. Marshall and published by Springer. This book was released on 2006-11-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

TB Algebra (Kanpur) Unified

Author : A. R. Vasishtha
Publisher : Krishna Prakashan Media
ISBN 13 : 818283564X
Total Pages : 373 pages
Book Rating : 4.1/5 (828 download)

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Book Synopsis TB Algebra (Kanpur) Unified by : A. R. Vasishtha

Download or read book TB Algebra (Kanpur) Unified written by A. R. Vasishtha and published by Krishna Prakashan Media. This book was released on with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Canadian Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1970 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A First Course in Abstract Algebra

Author : Marlow Anderson
Publisher : CRC Press
ISBN 13 : 1482245531
Total Pages : 547 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A First Course in Abstract Algebra by : Marlow Anderson

Download or read book A First Course in Abstract Algebra written by Marlow Anderson and published by CRC Press. This book was released on 2014-11-07 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like its popular predecessors, this text develops ring theory first by drawing on students' familiarity with integers and polynomials. This unique approach motivates students in studying abstract algebra and helps them understand the power of abstraction. This edition makes it easier to teach unique factorization as an optional topic and reorganizes the core material on rings, integral domains, and fields. Along with new exercises on Galois theory, it also includes a more detailed treatment of permutations as well as new chapters on Sylow theorems.