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In the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.
We describe groups of singular elements of quadratic extensions of global fields with odd class number. Using this description we then examine the Witt equivalence of rings of algebraic integers of nonreal bicyclic number fields and their analog in bicyclic function fields.
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