References

ISOTROPY OF SOME QUADRATIC FORMS AND ITS APPLICATIONS ON LEVELS AND SUBLEVELS OF ALGEBRAS


[1] R. B. Brown, On generalized Cayley-Dickson algebras, Pacific J. Math. 20(3) (1967), 415-422.

[2] E. Dieterich, Real quadratic division algebras, Comm. Algebra 28(2) (2000), 941-947.

[3] R. Elman and T. Y. Lam, Pfister forms and K-theory of fields, J. Alg. 23 (1972), 181-213.

[4] C. Flaut, Division algebras with dimension Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 13(2) (2006), 31-38.

[5] D. W. Hoffman, Isotropy of quadratic forms over the function field of a quadratic, Mathematische Zeitschrift 220(3) (1995), 461-476.

[6] D. W. Hoffman, Levels of quaternion algebras, Archiv der Mathematik 90(5) (2008), 401-411.

[7] D. W. Hoffman, Levels and sublevels of quaternion algebras, Mathematical Proceedings of the Royal Irish Academy 110A(1) (2010), 95-98.

[8] M. Knebusch, Generic splitting of quadratic forms I, Proc. London Math. Soc. 33 (1976), 65-93.

[9] P. Koprowski, Sums of squares of pure quaternions, Proc. Roy. Irish Acad. 98(1) (1998), 63-65.

[10] M. Küskemper and A. Wadsworth, A quaternion algebra of sublevel 3, Bull. Soc. Math. Belg. Sér. B 43(2) (1991), 181-185.

[11] A. Laghribi and P. Mammone, On the level of a quaternion algebra, Comm. Algebra 29(4) (2001), 1821-1828.

[12] D. B. Leep, Levels of division algebras, Glasgow Math. J. 32 (1990), 365-370.

[13] D. W. Lewis, Levels and sublevels of division algebras, Proc. Roy. Irish Acad. Sect. A 87(1) (1987), 103-106.

[14] D. W. Lewis, Levels of quaternion algebras, Rocky Mountain J. Math. 19 (1989), 787-792.

[15] J. M. Osborn, Quadratic division algebras, Trans. Amer. Math. Soc. 115 (1962), 202-221.

[16] J. O’ Shea, Levels and sublevels of composition algebras, Indag. Math. 18(1) (2007), 147-159.

[17] J. O’ Shea, Bounds on the levels of composition algebras, Mathematical Proceedings of the Royal Irish Academy 110A(1) (2010), 21-30.

[18] A. Pfister, Zur Darstellung von-I als Summe von quadraten in einem Körper, J. London Math. Soc. 40 (1965), 159-165.

[19] S. Pumplün, Sums of squares in octonion algebras, Proc. Amer. Math. Soc. 133 (2005), 3143-3152.

[20] R. D. Schafer, On the algebras formed by the Cayley-Dickson process, Amer. J. Math. 76 (1954), 435-446.

[21] R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966.

[22] W. Scharlau, Quadratic and Hermitian Forms, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985.