论域与超域的边界，第二部分——7阶超域的枚举与分类
On the borderline of fields and hyperfields, part II -- Enumeration and classification of the hyperfields of order 7
AI总结：
本文作为系列第二部分，构造并枚举了所有7阶超域，揭示了7元典范超群族，并基于简化公理的新定义降低了计算验证成本，同时完善了斜超域等性质。
摘要：
商超域是域与超域边界上的一个里程碑。本文是我们先前发表论文的第二部分，构造、枚举并呈现了所有7阶超域，在此过程中揭示了一个重要的7元典范超群族。对这些超域的研究证明了其中既存在商超域也存在非商超域。它们的构造之所以可行，是因为基于本文引入的一个具有更少公理的新超域定义，此前我们证明了可逆性公理可以从超域的其他公理推导出来。因此，计算机测试一个结构是否为超域所需的处理能力大大降低。本文还证明了斜超域、强典范超域/超环和优典范超域/超环的性质并给出了相关例子，这些内容总结并完善了第一部分先前发表的结论和结果。
英文摘要：
The quotient hyperfield is a landmark on the borderline of fields and hyperfields. In this paper, which is the second part of our previously published paper, all the hyperfields of order 7 are constructed, enumerated and presented, in the course of which an important family of 7-element canonical hypergroups is revealed. The study of these hyperfields proved the existence of both quotient and non-quotient ones among them. Their construction became feasible because it is based on a new definition of the hyperfield with fewer axioms, which is introduced in this paper following our proof that the axiom of reversibility can derive from the other axioms of the hyperfield. Hence, the processing power needed for a computer to test whether a structure is a hyperfield or not is much less. This paper also proves properties and contains examples of skew hyperfields, strongly canonical hyperfields/hyperrings and superiorly canonical hyperfields/hyperrings that wrap up and complete the previously published conclusions and results of its first part.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
