Miniquaternion geometry : an introduction to the study of projective planes
著者
書誌事項
Miniquaternion geometry : an introduction to the study of projective planes
（Cambridge tracts in mathematics and mathematical physics, no. 60）
Cambridge Univ. Press, 1971
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注記
Bibliography: p. 171-173
Includes index
内容説明・目次
内容説明
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.
目次
- 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 and D
- 5. The plane .
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