Characteristic, C-Characteristic and Positive Cones in Hyperfields

Dawid Edmund Kędzierski, Alessandro Linzi () and Hanna Stojałowska
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Dawid Edmund Kędzierski: Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
Alessandro Linzi: Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
Hanna Stojałowska: Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Mathematics, 2023, vol. 11, issue 3, 1-20

Abstract: We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for deciding whether certain hyperfields cannot be obtained via Krasner’s quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for the C-characteristic. Finally, we study the (directed) graph associated with the strict partial order induced by a positive cone in a hyperfield in various examples.

Keywords: hyperfield; positive cone; order; characteristic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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