Results 41 to 50 of about 110 (80)
, 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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Perfect matroids over hyperfields
arXiv, 2019 19 ...
Bowler, Nathan, Pendavingh, Rudi A.
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On the structure of hyperfields obtained as quotients of fields
Proceedings of the American Mathematical Society, 2020 We determine all isomorphism classes of hyperfields of a given finite order which can be obtained as quotients of finite fields of sufficiently large order. Using this result, we determine which hyperfields of order at most 4 are quotients of fields.
Baker, Matthew, Jin, Tong
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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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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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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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Hypergroups and hyperfields in universal algebra
, 2016 Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer the general theory from universal algebra. Special attention is given to the examples from Baker's article.
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On the asymptotic behavior of finite hyperfields
21 pages, 1 ...
Le, Tuong, Lowen, Chayim
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Convex geometry over ordered hyperfields
Innovations in Incidence Geometry: Algebraic, Topological and CombinatorialWe initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields arising as quotients of fields. We prove hyperfield analogues of Helly, Radon and Carathéodory theorems. We also show that arbitrary convex sets can be separated via hemispaces.
Maxwell, James, Smith, Ben
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