Results 71 to 80 of about 394 (102)

Field extensions, Derivations, and Matroids over Skew Hyperfields

arXiv, 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^ $ on ground set $E$ with coefficients in a certain skew hyperfield $L^ $. This skew hyperfield $L^ $ is defined in terms of $L$ and its Frobenius action $ :x\mapsto x^p$.
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Generalising Kapranov's theorem for tropical geometry over hyperfields [PDF]

Journal of Algebra
22 pages Corrections to Typos.
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Realization spaces of matroids over hyperfields

, 2015
We study realization spaces of matroids over hyperfields (in the sense of Baker and Bowler). More precisely, given a matroid M and a hyperfield H we determine the space of all H-matroids over M. This can be seen as the matroid stratum of the hyperfield Grassmannians in the sense of Anderson and Davis. We give different descriptions of these realization
Delucchi, Emanuele, Hoessly, Linard, Saini, Elia   +2 more
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Blocks in Finite Hyperfields

15 ...
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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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Small weak hyperfields in hadronic mechanics

Ratio Mathematica
It was in mid 90es when Professor R. M. Santilli realized, for the first time, that his innovating theories can be appropriate expressed by multi-valued systems. At that time the largest class of hyper-structures, the Hv-structures, based on the weak properties, were introduced and studied deeply.
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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
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Hypernorm on hypervector spaces over a hyperfield

The Journal of Analysis
AbstractHypernorm is a generalization of the notion of a norm on a vector space over a field. In this paper, we consider a hypervector space $$(\mathbb {V}, +)$$ ( V , + ) over a hyperfield, where $$+
P. Pallavi, S. P. Kuncham, S. Tapatee, B. Vadiraja, P. K. Harikrishnan   +4 more
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On the borderline of fields and hyperfields, part Ⅱ – Enumeration and classification of the hyperfields of order 7

AIMS Mathematics
127 pages, 305 tables Subj-class: math.RA - Rings and Algebras MSC-class: 16Y20 (Primary); 20N20 (Secondary) We extend the results of our previous papers and we reduce the axioms of the definition of the hyperfield. This facilitates the construction, enumeration and classification of all the hyperfields of order 7, while also revealing an important ...
Massouros, Christos G., Massouros, Gerasimos G.   +1 more
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A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception. [PDF]

Vision (Basel), 2018
Neilson PD, Neilson MD, Bye RT.
europepmc   +1 more source