ANISOTROPIC FORMS OF HIGHER DEGREE UNDER FINITE DIMENSIONAL FIELD EXTENSIONS

作者：Johnson A; Pumpluen S^*

来源：Communications in Algebra, 2010, 38(6): 2064-2078.

DOI：10.1080/00927870903023113

• Anisotropic forms
• Forms of higher degree
• Homogeneous polynomials
• Nontrivial zeros
• Springer's theorem

Let F be a field of characteristic 0 or greater than d. We investigate anisotropic forms of degree d > 2 and their behaviour under field extensions of degree coprime to d. A form of degree d over F which permits composition or Jordan composition remains anisotropic under any field extension of degree coprime to d. Other classes of forms are constructed which stay anisotropic under such extensions.

• 出版日期2010