Anisotropic Forms of Higher Degree Under Finite Dimensional Field Extensions

REFERENCES

• Ayad , M. , Hellegouarch , Y. ( 1989 ). Autour d'un théorèm de Springer. C.R. Acad. Sci. Paris, t. 309, Série 1 Math., no. 4, 209–211 .
   Google Scholar
• Draxl , P. ( 1983 ). Skew Fields . Cambridge : Cambridge University Press .
   Google Scholar
• Harrison , D. K. ( 1975 ). A Grothendieck ring of higher degree forms . J. Algebra 35 : 123 – 138 .
   Web of Science ®Google Scholar
• Harrison , D. K. , Pareigis , B. ( 1988 ). Witt rings of higher degree forms . Comm. Alg. 16 ( 6 ): 1275 – 1313 .
   Web of Science ®Google Scholar
• Jacobson , N. ( 1968 ). Structure and Representations of Jordan Algebras . AMS Coll. Publ. 39 , Providence, RI : AMS .
   Google Scholar
• Jacobson , N. ( 1983 ). Some applications to Jordan norms to involutorial simple associate algebras . Adv. Math. 48 : 149 – 165 .
   Google Scholar
• Knus , M. A. , Merkurjev , A. , Rost , M. , Tignol , J.-P. ( 1998 ). The Book of Involutions . Vol. 44 , Providence, RI : AMS Coll. Publications .
   Google Scholar
• Lam , T. Y. ( 2004 ). Introduction to Quadratic Forms over Fields . Graduate Studies in Mathematics , Vol. 67, Rhode Island : AMS Providence .
   Google Scholar
• Lang , S. ( 1965 ). Algebra . Reading : Addison-Wesley .
   Google Scholar
• McCrimmon , K. ( 2004 ). A Taste of Jordan Algebras . New York : Universitext, Springer Verlag .
   Google Scholar
• Petersson , H. P. , Racine , M. ( 1996 ). An elementary approach to the Serre-Rost invariant of Albert algebras . Indag. Math., N. S. 7 ( 3 ): 343 – 365 .
   Web of Science ®Google Scholar
• Petersson , H. P. , Racine , M. ( 1997 ). The Serre-Rost invariant of Albert algebras in characteristic three . Indag. Math. N. S. 8 ( 4 ): 543 – 548 .
   Web of Science ®Google Scholar
• Pierce , R. S. ( 1982 ). Associative Algebras . Graduate Texts in Mathematics 88 , Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Pumplün , S. Some classes of multiplicative forms of higher degree . Comm. Alg. 37 : 609 – 629 .
   Google Scholar
• Pumplün , S. Round Forms of Higher Degree . Preprint, submitted.
   Google Scholar
• Pumplün , S. , The Behaviour of Albert Division Algebras under Field Extensions of Degree Coprime to 3. Jordan Theory Preprint Archives: http://homepage.uibk.ac.at/~c70202/jordan/index.html. Accessed April 26, 2010.
   Google Scholar
• Saltman , D. J. ( 1998 ). Lectures on Division Algebras . Rohde Island : AMS Providence .
   Google Scholar
• Schafer , R. D. ( 1970 ). Forms permitting composition . Adv. Math. 4 : 127 – 148 .
   Web of Science ®Google Scholar
• Scharlau , W. ( 1985 ). Quadratic and Hermitian Forms . Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Schmähling , R. ( 1974 ). Hintereinanderausführung von Formen . J. Reine Angew. Math. 272 : 113 – 126 .
   Google Scholar
• Communicated by S. Sehgal.
   Google Scholar