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Miniquaternion Geometry

An Introduction to the Study of Projective Planes

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Paperback | 27 November 2008

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188 Pages

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21.7 x 14.2 x 1.2

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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.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Mathematical Foundation Set Theory Calculus & Mathematical Analysis Geometry Applied Mathematics Topology

Algebraic Background
Two algebraic systems with nine elements
Field-Planes
Projective planes
Galois planes of orders 3 and 9
Miniquaternion Planes
The planes +¼ and +¼D
The plane +
Table of Contents provided by Publisher. All Rights Reserved.

Miniquaternion Geometry

An Introduction to the Study of Projective Planes

At a Glance

Paperback

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How to return your order

Defective items

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