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Recent results in hyperring and hyperfield theory. (English) Zbl 0655.16027

Author’s abstract: “This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the “sums” of two elements is a subset of the structure. The results in this paper show that these structures cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and hyperrings cannot be derived from the corresponding results in field and ring theory.”
Reviewer: B.Pondělíček

MSC:

16Y60 Semirings
12K99 Generalizations of fields
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