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Cambridge Tracts in Mathematics #60: Miniquaternion Geometry

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Cambridge Tracts in Mathematics #60: Miniquaternion Geometry Cover

 

Synopses & Reviews

Publisher Comments:

This tract provides an introduction to four finite geometrical systems and to the theory of projective planes. Of the four geometries, one is based on a nine-element field and the other three can be constructed from the nine-element 'miniquaternion algebra', a simple system which has many though not all the properties of a field. The three systems based on the miniquaternion algebra have widely differing properties; none of them has the homogeneity of structure which characterizes geometry over a field. While these four geometries are the main subject of this book, many of the ideas developed are of much more general significance. The authors have assumed a knowledge of the simpler properties of groups, fields, matrices and transformations (mappings), such as is contained in a first course in abstract algebra. Development of the nine-element field and the miniquaternion system from a prescribed set of properties of the operations of addition and multiplication are covered in an introductory chapter. Exercises of varying difficulty are integrated with the text.

Table of Contents

Part I. Algebraic Background: 1. Two algebraic systems with nine elements; Part II. Field-Planes: 2. Projective planes; 3. Galois planes of orders 3 and 9; Part III. Miniquaternion Planes: 4. The planes Ω and ΩD; 5. The plane Ψ.

Product Details

ISBN:
9780521090643
Author:
Room, T. G.
Publisher:
Cambridge University Press
Author:
Kirkpatrick, P. B.
Location:
Cambridge
Subject:
Geometry - General
Subject:
Applied
Subject:
Topology - General
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Topology
Edition Description:
Trade paper
Series:
Cambridge Tracts in Mathematics
Series Volume:
60
Publication Date:
20081131
Binding:
TRADE PAPER
Language:
English
Pages:
188
Dimensions:
5.51x8.50x.43 in. .54 lbs.

Related Subjects

Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Cambridge Tracts in Mathematics #60: Miniquaternion Geometry New Trade Paper
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Product details 188 pages Cambridge University Press - English 9780521090643 Reviews:
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