A Witt Theorem for Non-Defective Lattices
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 499-511

Voir la notice de l'article provenant de la source Cambridge University Press

In [10], Witt laid the foundation for the study of quadratic forms over fields. Suppose Q is a quadratic form defined on a finite dimensional vector space V over a field of characteristic not equal to 2. Witt showed that non-zero vectors x and y in V satisfying Q(x) = Q(y) can be mapped into each other via an isometry of the vector space V. More generally, if τ : W⟶ W’ is an isometry between subspaces of V, then τ extends to an isometry φ of V.
Morin-Strom, Karl A. A Witt Theorem for Non-Defective Lattices. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 499-511. doi: 10.4153/CJM-1978-045-5
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[1] 1. Band, M., On the integral extensions of quadratic forms over local fields, Can. J. Math. 22 (1970), 297–307. Google Scholar

[2] 2. Cohen, D. M., Witt's theorem for quadratic forms, Conference on Quadratic Forms, Queen's Papers in Mathematics, 46 (1977), 406–411. Google Scholar

[3] 3. Hsia, J. S., note on the integral equivalence of vectors in characteristic 2, Math. Ann. 179 (1968), 63–69. Google Scholar

[4] 4. Hsia, J. S., One dimensional Witt's theorem over modular lattices, Bull. Amer. Math. Soc. 76 (1970), 113–115. Google Scholar

[5] 5. James, D. G. and Rosenzweig, S. M., Associated vectors in lattices over valuation rings, Amer. J. Math. 90 (1968), 295–307. Google Scholar

[6] 6. Kneser, M., Witts Satz fur quadratische Formen uber lokalen Ringen, Nachr. die Akad. der Wiss. Gottingen, Math.-Phys. II Heft 9 (1972), 195–203. Google Scholar

[7] 7. O'Meara, O. T., Introduction to quadratic forms, Grundlchren der Math. Wiss. (Springer-Verlag, Berlin 1971). Google Scholar

[8] 8. Rosenzweig, S. M., An anology of Witt's theorem for modules over the ring of p-adic integers, Ph.D. thesis, M.I.T. (1958). Google Scholar

[9] 9. Trojan, A., The integral extension of isometrics of quadratic forms over local fields, Can. J. Math. 18 (1966), 920–942. Google Scholar

[10] 10. Witt, E., Théorie der quadratischen Formen in beliebigen Korpen, Journal fur die reine und angewandte Math. 176 (1937), 31–44. Google Scholar

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