Abstract
Let R be a commutative semilocal ring in which 2 is a unit. It is further assumed that either R has no residue fields with 5 or fewer elements, or squares of units may be lifted modulo the Jacobson radical of R. Generalizing a theorem of Elman and Lam, it is proved that quadratic forms over R are characterized by their Hasse invariant, determinant and rank iff I 3( R) = 0, where I( R) is the ideal generated by forms of even rank in the Witt ring of R.
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