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Splitting of Quadratic Forms under Some Generic Field Extensions

Research paper by A. S. Sivatski

Indexed on: 01 Nov '04Published on: 01 Nov '04Published in: Journal of Mathematical Sciences



Abstract

Let F be a field, char F ≠ 2, and ϕ and ψ be anisotropic quadratic forms over F. Let L be a generic field extension of F such that i(ψL) ≥ 2. Under what conditions is the form ϕL isotropic? We give an answer to this question in the cases where dim ϕ = 5, dim ψ = 6 and dim ϕ = 6, dim ψ = 7. Bibliography: 18 titles.