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Partially Ordered Rings and Semi-Algebraic Geometry : Cambridge Introduction to the History of Mankind - Gregory W. Brumfiel

Partially Ordered Rings and Semi-Algebraic Geometry

Cambridge Introduction to the History of Mankind

Paperback

Published: 18th February 1980
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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.

Introduction
Partially Ordered Rings
Homomorphisms and Convex Ideals
Localization
Some Categorical Notions
The Prime Convex Ideal Spectrum
Polynomials
Ordered Fields
Affine Semi-Algebraic Sets
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521228459
ISBN-10: 052122845X
Series: Cambridge Introduction to the History of Mankind
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 292
Published: 18th February 1980
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.68
Weight (kg): 0.43