Miniquaternion Geometry: An Introduction to the Study of Projective Planes (Cambridge Tracts in Mathematics #60) (Paperback)

Miniquaternion Geometry: An Introduction to the Study of Projective Planes (Cambridge Tracts in Mathematics #60) By T. G. Room, P. B. Kirkpatrick Cover Image
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Description


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.


Product Details
ISBN: 9780521090643
ISBN-10: 0521090644
Publisher: Cambridge University Press
Publication Date: November 27th, 2008
Pages: 188
Language: English
Series: Cambridge Tracts in Mathematics