论文标题
一般的Arason-Pfister Hauptsatz
The general Arason-Pfister Hauptsatz
论文作者
论文摘要
In the present we develop a fragment of the theory of superfields, polynomials and Marshall's quotient in order to obtain for general special groups, a proof of the Arason-Pfister Hauptsatz (APH): "if $ϕ\neq \emptyset$ is an anisotropic form and $ϕ\in I^n(F)$ then $dim (ϕ) \geq 2^n$".在此过程中，我们还为减少的特殊组获得了APH的替代证明，以避免在\ cite {dickmann2000special}中开发的不变性。完整的Arason-Pfister Hauptsatz的应用带来了与特殊组/高场相关的分级环的有趣属性。 \ textbf {关键字：} Arason-Pfister Hauptsatz; Hyperfields；特殊团体； Milnor K理论；分级戒指。
In the present we develop a fragment of the theory of superfields, polynomials and Marshall's quotient in order to obtain for general special groups, a proof of the Arason-Pfister Hauptsatz (APH): "if $ϕ\neq \emptyset$ is an anisotropic form and $ϕ\in I^n(F)$ then $dim (ϕ) \geq 2^n$". In the process, we also obtain an alternative proof of APH for reduced special groups that avoid the uses of the invariants developed in \cite{dickmann2000special}. The applications of the full Arason-Pfister Hauptsatz leads to interesting properties of graded rings associated to special groups/hyperfields. \textbf{Keywords:} Arason-Pfister Hauptsatz; hyperfields; special groups; Milnor K-theory; graded rings.
