Miniquaternion Geometry

An Introduction to the Study of Projective Planes

T. G. Room, P. B. Kirkpatrick (Autoren)

Buch | Hardcover

184 Seiten

1971
Cambridge University Press (Verlag)
978-0-521-07926-6 (ISBN)

Infos

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.

Inhalt

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 Ω and ΩD; 5. The plane Ψ.

Produkt-Details

• Erscheint lt. Verlag: 2.1.1971
• Reihe/Serie: Cambridge Tracts in Mathematics
• Zusatzinfo: Worked examples or Exercises
• Verlagsort: Cambridge
• Sprache: englisch
• Gewicht: 340 g
• Themenwelt: Mathematik / Informatik ► Mathematik
• ISBN-10: 0-521-07926-8 / 0521079268
• ISBN-13: 978-0-521-07926-6 / 9780521079266
• Zustand: Neuware