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Miniquaternion Geometry: An Introduction to the Study of Projective Planes by T. G. Room, P. B. Kirkpatrick

Miniquaternion Geometry: An Introduction to the Study of Projective Planes

by T. G. Room , P. B. Kirkpatrick
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Book cover type: Paperback
  • ISBN13: 9780521090643
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 188
  • Original Price: GBP 40.0
  • Language: English
  • Edition: 1
  • Item Weight: 245 grams
  • BISAC Subject(s): Geometry / General

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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