Description

January 2nd 1971 | Hardcover | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 184 pages | ISBN: 9780521079266 | 10.39 Mb

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 miniquaternionMoreThis 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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