In this paper, first we introduce n-polygroups and characterize 2-polygroups of order 4 up to isomorphism. Then using 2-polygroups we introduce 2-Krasner hyperfields and we show that there exactly exists one 2-Krasner hyperfield of order 4. Moreover, we propose a hyperfield of order 4 which is not as a quotient hyperfield $${F \over G}$$ . Finally, some programs written in MATLAB which are based on obtained results compute the number of polygroups, weak polygroups and Krasner hyperfields of order 4 up to isomorphism.

中文翻译：

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4阶克拉斯纳超场的分类

在本文中，我们首先介绍 n-polygroups 并表征 4 阶至同构的 2-polygroups。然后使用 2-polygroups 我们引入 2-Krasner 超场，我们证明确实存在一个 4 阶的 2-Krasner 超场。此外，我们提出了一个 4 阶的超场，它不是商超场 $${F \over G }$$ 。最后，一些用 MATLAB 编写的程序根据获得的结果计算多群、弱多群和 4 阶至同构的 Krasner 超场的数量。