Quadratic spaces over discrete Hodge algebras
A and R are commutative Noetherian rings with 2 invertible; R is a ''discrete Hodge algebra'' over A if \(R\cong A[X_ 0,...,X_ n]/I\) for an ideal I generated by monomials. Theorem 1: If A is a Dedekind domain, any quadratic space over R which contains a unimodular isotropic element comes by base extension from A. Theorem 2: Let q be a quadratic space over R and assume Witt index of \(q\geq \dim R>\dim A,\) then q is cancellative. These theorems generalize results of \textit{R. Parimala} [Am. J. Math. 103, 289-296 (1981; Zbl 0466.13007) and Commun. Algebra 12, 229- 238 (1984; Zbl 0532.10015)].
scientific article; zbMATH DE number 3973011