Geodesic
Abstract Quadratic Forms
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1218-1233

Voir la notice de l'article provenant de la source Cambridge University Press

We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence relation on unordered n-ples of G. For n = 2: (a, b) ~ (c, d) if a + b = c + d and ab = cd. For n > 2 we define equivalence “piecewise”: there is to be a chain from (a 1, ..., an ) to (b 1, ..., bn ) where at each step only two elements are changed in accordance with the equivalence just defined for n = 2. 
Kaplansky, Irving; Shaker, Richard J. Abstract Quadratic Forms. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1218-1233. doi: 10.4153/CJM-1969-134-5
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[1] 1. Albert, A. A., Symmetric and alternate matrices in an arbitrary field, Trans. Amer. Math- Soc. 43 (1938), 386–436. Google Scholar

[2] 2. Knight, J. T., Quadratic forms over R(t), Proc. Cambridge Philos. Soc. 62 (1966), 197–205. Google Scholar

[3] 3. Scharlau, Winfried, Quadratische Formen und Galois-Cohomologie, Invent. Math. 4 (1967), 238–264. Google Scholar

[4] 4. Shaker, R. J., Abstract quadratic forms, Thesis, University of Chicago, Chicago, Illinois, 1968. Google Scholar

[5] 5. Witt, E., Théorie der quadratischen Formen in beliebigen Kôrpern, J. Reine Angew. Math. 176 (1937), 31–44. Google Scholar

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