Buch, Englisch, Band 60, 184 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 245 g
An Introduction to the Study of Projective Planes
Buch, Englisch, Band 60, 184 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 245 g
Reihe: Cambridge Tracts in Mathematics
ISBN: 978-0-521-09064-3
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Weitere Infos & Material
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 O and OD; 5. The plane ?.
