This classic work (first published in 1947), in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasized throughout. This first volume is divided into two parts. The first is devoted to pure algebra: the basic notions, the theory of matrices over a non-commutative ground field and a study of algebraic equations. The second part is in n dimensions. It concludes with a purely algebraic account of collineations and correlations.
Reviews & endorsements
'This treatise … is notable for its clarity of treatment and for the rigour of its demonstrations, and will repay careful study even in those parts which deal with matters generally considered familiar.' NatureSee more reviews
'The book is well set out, and is a pleasure to work through.' The Times Literary Supplement
'Motivations are given. Examples of significant and useful varieties are numerous. All the algebra needed is given, and, what is more, these books tell how to translate geometry into algebra, and conversely.' Bulletin of the American Mathematical Society
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- Date Published: April 1994
- format: Paperback
- isbn: 9780521469005
- length: 452 pages
- dimensions: 228 x 151 x 29 mm
- weight: 0.73kg
- availability: Available
Table of Contents
Book I. Algebraic Preliminaries:
1. Rings and fields
2. Linear algebra, matrices, determinants
3. Algebraic dependence
4. Algebraic equations
Book II. Projective Space:
5. Projective space: algebraic definition
6. Projective space: synthetic definition
7. Grassmann coordinates
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