Geodesic
A Note on Quadratic forms Over Arbitrary Semi-Local Rings
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 513-527

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

Let R be a commutative ring. A bilinear space (E, B) over R is â finitely generated projective R-module E together with a symmetric bilinear mapping B:E X E →R which is nondegenerate (i.e. the natural mapping E → HomR(E} R) induced by B is an isomorphism). A quadratic space (E, B, ) is a bilinear space (E, B) together with a quadratic mapping φ:E →R such that B(x, y) = φ (x + y) — φ (x) — φ (y) and φ (rx) = r2φ (x) for all x, y in E and r in R. If 2 is a unit in R, then φ (x) = 1⁄2. B{x,x) and the two types of spaces are in obvious 1 — 1 correspondence. 
Mandelberg, K. I. A Note on Quadratic forms Over Arbitrary Semi-Local Rings. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 513-527. doi: 10.4153/CJM-1975-063-7
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