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Look Inside Miniquaternion Geometry

Miniquaternion Geometry
An Introduction to the Study of Projective Planes


Part of Cambridge Tracts in Mathematics

  • Date Published: November 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521090643

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About the Authors
  • 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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    Product details

    • Date Published: November 2008
    • format: Paperback
    • isbn: 9780521090643
    • length: 188 pages
    • dimensions: 216 x 140 x 11 mm
    • weight: 0.25kg
    • availability: Available
  • 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.

  • Authors

    T. G. Room

    P. B. Kirkpatrick

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