Results 61 to 70 of about 239 (103)
Hyperfields for Tropical Geometry I. Hyperfields and dequantization
, 2010 47 pages, 5 figures, the previous version has been radically changed in order to add new references and correct ...
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, 2019 We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong hyperfield extensions.
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On the hyperfields associated to valued fields
, 2022 One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field.
Touchard, Pierre, Linzi, Alessandro
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Field extensions, derivations, and matroids over skew hyperfields [PDF]
, 2018 We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$ for $e\in E$ gives rise to a matroid $M^\sigma$ on ground set $E$ with coefficients in a certain skew hyperfield $L^\sigma$.
Pendavingh, R., Pendavingh, RA Rudi
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On the borderline of fields and hyperfields, part II -- Enumeration and classification of the hyperfields of order 7 [PDF]
The quotient hyperfield is a landmark on the borderline of fields and hyperfields. In this paper, which is the second part of our previously published paper, all the hyperfields of order 7 are constructed, enumerated and presented, in the course of which
Massouros, Gerasimos G. +1 more
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Tropical geometry over the tropical hyperfield
Rocky Mountain Journal of Mathematics, 2022 In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a nonarchimedean absolute value can be considered as a morphism into the tropical hyperfield.
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Hyperfields and their applications in tropical geometry or matroid theory
, 2023 Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to classical fields, summation in a hyperfield is multivalued, that is, the sum of two elements is not a single element, but a whole set of elements ...
Andr, Břetislav
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The Riemannian Geometry Theory of Visually-Guided Movement Accounts for Afterimage Illusions and Size Constancy. [PDF]
Vision (Basel), 2022 Neilson PD, Neilson MD, Bye RT.
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Hypervaluations on Hyperfields and Ordered Canonical Hypergroups
Journal of Mathematical Sciences and InformaticsWe study the concept of hypervaluations on hyperfields. In particular, we show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of a hypervaluation onto an ordered abelian group (which induces the same valuation hyperring) and an order preserving homomorphism of hypergroups.
Linzi, Alessandro, Stojałowska, Hanna
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A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement. [PDF]
Vision (Basel), 2021 Neilson PD, Neilson MD, Bye RT.
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