关于作为有限域商的超域的特征
On Characteristics of Hyperfields Obtained as Quotients of Finite Fields
摘要：
超结构是正则代数结构的自然扩张，其中一个运算称为超运算，是多值的;超域是域上的这种扩展。M. Krasner（1962）证明了商$\mathbb{F}_p/G$是一个超域，其中$G$是$\mathbb{F}_p$中单位的子群。场的特征可以从场的阶显式地确定，但是不存在用于确定$\mathbb{F}_p/G$形式的超场的特征的现有推广。证明了对于奇素数$p$，超域$\mathbb{F}_p/G$和$|G|=1,2,3,4$的特征存在一个显式形式.最后，我们证明了$|G|$是素数的超域的特征的一般形式。
英文摘要：
Hyperstructures are a natural extension of regular algebraic structures in which one of the operations, known as the hyperoperation, is multivalued; a hyperfield is such an extension on a field. M. Krasner (1962) proved that the quotient $\mathbb{F}_p/G$, where $G$ is a subgroup of units in $\mathbb{F}_p$ is a hyperfield. The characteristic of a field may be explicitly determined from the order of the field, but there are no existing generalizations for determining the characteristic of a hyperfield of the form $\mathbb{F}_p/G$. We show that for odd primes $p$, there exists an explicit form for the characteristic of the hyperfield $\mathbb{F}_p/G$ and $|G|=1,2,3,4$. Finally, we prove a general form of the characteristic for hyperfields where $|G|$ is prime.
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