Let k be a field of characteristic not two, let f x , x gk x , x be an h 0 1 0 1 irreducible homogeneous polynomial and denote the ring of elements of degree w x w x zero in the homogeneous localization k x , x by k x , x . For deg f s 3 it 0 1 f 0 1 Žf . h h h w x is proved that the composition alg
Composition Algebras over a Ring of Fractions
✍ Scribed by S. Pumplün
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 242 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
Using some theorems on composition algebras over rings of genus zero and elementary results from algebraic geometry, all composition algebras over a ring of fractions related to the projective line over a field are enumerated and partly classified.
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