Abstract
This article considers the splitting properties of finite-dimensional division rings over universal splitting fields of quadratic forms. An example of a field with u-invariant equal to 6 is constructed, which contradicts Kaplansky's conjecture concerning u-invariants.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 75–89, 1989.
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Merkur'ev, A.S. Kaplansky conjecture in the theory of quadratic forms. J Math Sci 57, 3489–3497 (1991). https://doi.org/10.1007/BF01100118
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DOI: https://doi.org/10.1007/BF01100118