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1.
A result of Krasner in categorial form
Alessandro Linzi, 2023, original scientific article

Keywords: valuation, completion, field, hyperfield, category theory
Published in RUNG: 11.12.2023; Views: 577; Downloads: 6
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2.
Algebraic structures and graph theory
scientific monograph

Keywords: graphs, Cayley graph, graph energy, hypergraphs, semigroups, algebra, hypergroups, hyperfield
Published in RUNG: 10.08.2023; Views: 761; Downloads: 7
.pdf Full text (4,26 MB)
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3.
A new symmetry in valuation theory
Alessandro Linzi, 2023, published scientific conference contribution abstract

Keywords: valuation, valued field, p-adic numbers, hyperfield
Published in RUNG: 27.06.2023; Views: 909; Downloads: 8
.pdf Full text (405,62 KB)

4.
Valuations on structures more general than fields
Alessandro Linzi, 2023, published scientific conference contribution

Keywords: hyperfield, valuation, valued field, tropical hyperfield
Published in RUNG: 27.06.2023; Views: 804; Downloads: 8
.pdf Full text (276,86 KB)
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5.
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: 968; Downloads: 3
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6.
Algebraic hyperstructures in the model theory of valued fields : PhD in mathematics
Alessandro Linzi, 2022, doctoral dissertation

Keywords: hyperfield, valued field, algebra, model theory, quantifier elimination
Published in RUNG: 27.10.2022; Views: 1315; Downloads: 80
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7.
Krasner hyperfields and the model theory of valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: hyperfield, valued field, model theory, quantifier elimination, valuation, subhyperfield
Published in RUNG: 10.10.2022; Views: 1010; Downloads: 0
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8.
Structures for relative quantifier elimination in valued fields : Algebraic hyperstructures in the model theory of valued fields
Alessandro Linzi, invited lecture at foreign university

Keywords: model theory, quantifier elimination, valued field, hyperfield
Published in RUNG: 10.10.2022; Views: 1035; Downloads: 0
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9.
Structures for quantifier elimination in valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: quantifier elimination, model theory, valued field, hyperfield
Published in RUNG: 10.10.2022; Views: 950; Downloads: 0
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10.
Krasner hyperfields and the model theory of valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: hyperfield, valued field, model theory, quantifier elimination
Published in RUNG: 07.10.2022; Views: 1124; Downloads: 0
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