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

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9780521079266: Miniquaternion Geometry: An Introduction to the Study of Projective Planes (Cambridge Tracts in Mathematics)
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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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Book 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.

About the Author:

Bela Bollobas has taught at Cambridge University's Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobas has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.

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Room, T. G., Kirkpatrick, P. B.
Published by Cambridge University Press (1971)
ISBN 10: 0521079268 ISBN 13: 9780521079266
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T. G. Room; P. B. Kirkpatrick
Published by Cambridge University Press (1971)
ISBN 10: 0521079268 ISBN 13: 9780521079266
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