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Generalisations of Tropical Geometry over Hyperfields [PDF]
, 2022 Hyperfields are structures that generalise the notion of a field by way of allowing the addition operation to be multivalued. The aim of this thesis is to examine generalisations of classical theory from algebraic geometry and its combinatorial shadow, tropical geometry.
JAMES MAXWELL
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Extension of elliptic curves on Krasner hyperfields
Communications in Algebra, 2019AbstractThe aim of the article is to initiate a new study in the framework of algebraic hyperfields, with an applicative impact in cryptography.
Vahid Vahedi +2 more
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A Field Theory Problem Relating to Questions in Hyperfield Theory
AIP Conference Proceedings, 2011 Ch Tsitouras, Zacharias Anastassi
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IFAC Proceedings Volumes, 1983
Abstract Basically, σ- hyperfields on σ- complete De Morgan algebras are introduced and explored. Measurable spaces (topological spaces) are extended to hypermeasurable spaces (hypertopological spaces) constructed considering σ- hyperfields. Random sets are then given a pure measure theoretical definition and, finally, random fuzzy sets are ...
Wang Pei-Zhuang, E. Sanchez
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Abstract Basically, σ- hyperfields on σ- complete De Morgan algebras are introduced and explored. Measurable spaces (topological spaces) are extended to hypermeasurable spaces (hypertopological spaces) constructed considering σ- hyperfields. Random sets are then given a pure measure theoretical definition and, finally, random fuzzy sets are ...
Wang Pei-Zhuang, E. Sanchez
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A hypervaluation of a hyperfield onto a totally ordered canonical hypergroup
Studia Scientiarum Mathematicarum Hungarica, 2015 S. Anvariyeh, Kh. Harijani
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Theory of hyperrings and hyperfields
Algebra and Logic, 1985The notion of hyperfield was introduced by \textit{M. Krasner} [Colloq. d'Algèbre Supérieure, CBRM, Bruxelles 1956, 129-206 (1959; Zbl 0085.265)] who raised the following question: Are all hyperfields isomorphic to quotient hyperfields? He also raised an analogous question for hyperrings.
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Hyperaffine planes over hyperfields
Journal of Geometry, 1995The authors first study hyperaffine planes coordinatized over planar hyperfields. The main purpose of the paper is to show that if an abstract hyperaffine plane satisfies certain additional conditions 1-11, then there exists a hyperfield such that the coordinate plane over this hyperfield is isomorphic to the given hyperaffine plane.
Procesi Ciampi, R., Rota, R.
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Journal of Algebraic Hyperstructures and Logical Algebras
The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences.
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The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences.
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1984
The concepts of (semi) hypergroups, hyperrings or hyperfields H differ from the ones of (semi) groups, rings, fields by replacing the operations of addition and multiplication by maps from H×H into the collection of nonempty subsets of H . A hyperring (H,∘,□) is complete if both (H,∘) and (H,□) are complete. The author gives examples for these concepts
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The concepts of (semi) hypergroups, hyperrings or hyperfields H differ from the ones of (semi) groups, rings, fields by replacing the operations of addition and multiplication by maps from H×H into the collection of nonempty subsets of H . A hyperring (H,∘,□) is complete if both (H,∘) and (H,□) are complete. The author gives examples for these concepts
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