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Characteristic, C-characteristic and positive cones in hyperfields
Dawid Edmund Kędzierski, Alessandro Linzi, Hanna Stojałowska, 2023, original scientific article

Abstract: We study the notions of positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We show how these interact in order to produce interesting results in the theory of hyperfields. For instance, we give 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 C-characteristic. Finally, we study the (directed) graph associated to the strict partial order induced by a positive cone in a hyperfield in various examples.
Keywords: hyperfield, order, characteristic, positive cone
Published in RUNG: 13.02.2023; Views: 1297; Downloads: 3
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Orderings and valuations in hyperfields
Katarzyna Kuhlmann, Alessandro Linzi, Hanna Stojałowska, 2022, original scientific article

Keywords: hyperfields, hyperring, ordering, valuation
Published in RUNG: 28.09.2022; Views: 1380; Downloads: 0
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