关于超环与Fuzzy环的关系
On the relation between hyperrings and fuzzy rings
摘要：
我们构造了一个完全嵌入的范畴的超域到Dress的范畴的模糊环，并明确描述了本质的形象-它未能在一个很小的方式本质上满射。这种嵌入提供了一个识别的贝克理论的拟阵的hyperfields与礼服的理论拟阵的模糊环（提供了一个限制，这些模糊环的基本形象）。嵌入函子从超域扩展到超环，我们详细研究了这种扩展。我们还分析了超域与Baker部分超域之间的关系。
英文摘要：
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially surjective in a very minor way. This embedding provides an identification of Baker's theory of matroids over hyperfields with Dress's theory of matroids over fuzzy rings (provided one restricts to those fuzzy rings in the essential image). The embedding functor extends from hyperfields to hyperrings, and we study this extension in detail. We also analyze the relation between hyperfields and Baker's partial demifields.
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