Geodesic
On Gleason's Definition of Quadratic Forms
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 233-236

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Suppose R is a commutative ring with identity. Let M be an R -module, and suppose f is a function from M to R. How do we characterize the property that f be a quadratic form? 
Davison, T. M. K. On Gleason's Definition of Quadratic Forms. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 233-236. doi: 10.4153/CMB-1981-036-4
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[1] 1. Gleason, A. M., The definition of a quadratic form. Amer. Math. Monthly. 73 (1966) 1049-1056. Google Scholar

[2] 2. Jacobson, N., Basic Algebra I. W. H. Freeman, San Francisco 1974. Google Scholar

[3] 3. Jordan, P. and von Neumann, J., On inner products in linear, metric spaces. Ann of Math. (2) 36 (1935) 719-723. Google Scholar

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