Results 51 to 60 of about 176 (118)

THE CLASS OF KRASNER HYPERFIELDS IS NOT ELEMENTARY

The Journal of Symbolic Logic
Abstract We show that the class of Krasner hyperfields is not elementary. To show this, we determine the rational rank of quotients of multiplicative groups in field extensions. We also discuss some related questions.
Błaszkiewicz, Piotr, Kowalski, Piotr
openaire   +2 more sources

Tropical Extensions and Baker-Lorscheid Multiplicities for Idylls

, 2023
In a recent paper, Matthew Baker and Oliver Lorscheid showed that Descartes's Rule of Signs and Newton's Polygon Rule can both be interpreted as multiplicities of polynomials over hyperfields.
Gunn, Trevor
core  

Extensions of Hyperfields

, 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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Helix-Hopes on Finite Hyperfields

Ratio Mathematica, 2016
Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We study the helix-hyperstructures on the representations using ordinary fields.
Vougiouklis, Thomas, Vougiouklis, Souzana   +1 more
openaire   +2 more sources

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
core   +1 more source

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
openaire   +3 more sources

Towards the horizons of Tits's vision -- on band schemes, crowds and F1-structures

, 2023
This text is dedicated to Jacques Tits's ideas on geometry over F1, the field with one element. In a first part, we explain how thin Tits geometries surface as rational point sets over the Krasner hyperfield, which links these ideas to combinatorial flag
Thas, Koen, Lorscheid, Oliver
core   +1 more source

Five golfers

, 1994
Five golfers -'Pam Holman, 5/10/94 ...
Holman, Pam;
core  

Sphingosine-1-phosphate expression in human epiretinal membranes. [PDF]

PLoS One, 2022
Kim M, Kwon S, Jeon S, Jung BJ, Kim KS.
europepmc   +1 more source

Hypervaluations on Hyperfields and Ordered Canonical Hypergroups

Journal of Mathematical Sciences and Informatics
We 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
openaire   +2 more sources