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A Note on Quadratic forms Over Arbitrary Semi-Local Rings

  • K. I. Mandelberg (a1)

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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 ER which is nondegenerate (i.e. the natural mapping EHomR(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) = ½. B﹛x,x) and the two types of spaces are in obvious 1 — 1 correspondence.

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References

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A Note on Quadratic forms Over Arbitrary Semi-Local Rings

  • K. I. Mandelberg (a1)

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