Results 1 to 10 of about 448 (100)
Methods of constructing hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1985 In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we give a negative answer to the question of whether every hyperfield is isomorphic to a quotient KG of a field K by some subgroup G of its multiplicative ...
Ch. G. Massouros
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A class of hyperrings and hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1983 Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H.
Marc Krasner
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On the Borderline of Fields and Hyperfields
Mathematics, 2023 The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is related ...
Gerasimos Massouros
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Characteristic, C-Characteristic and Positive Cones in Hyperfields
Mathematics, 2023 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.
Dawid Edmund Kędzierski +2 more
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Existence theorem of finite krasner hyperfields [PDF]
Journal of Hyperstructures, 2021 The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greaterthan or equal to 2.
Yuming Feng +3 more
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Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices.
Atamewoue Surdive +3 more
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Orderings and valuations in hyperfields
Journal of Algebra, 2022 We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induced on factor and residue hyperfields. Much of the theory from real fields can be generalized to real hyperfields; we point out facts that cannot. We generalize the Baer-Krull
Katarzyna Kuhlmann +2 more
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Hyperfields, truncated DVRs, and valued fields [PDF]
Journal of Number Theory, 2020 For any two complete discrete valued fields $K_1$ and $K_2$ of mixed characteristic with perfect residue fields, we show that if the $n$-th valued hyperfields of $K_1$ and $K_2$ are isomorphic over $p$ for each $n\ge1$, then $K_1$ and $K_2$ are isomorphic.
Junguk Lee
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Hyperhomographies on Krasner Hyperfields [PDF]
Symmetry, 2019 In this paper, we introduce generalized homographic transformations as hyperhomographies over Krasner hyperfields.These particular algebraic hyperstructues are quotient structures of classical fields modulo normal groups. Besides, we define some hyperoperations and investigate the properties of the derived hypergroups and H v -groups associated ...
Vahid Vahedi +2 more
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Journal of Algebra, 2021 26 pages, Final version to appear in Journal of ...
Jaiung Jun
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