Results 61 to 70 of about 110 (80)

Advanced results in enumeration of hyperfields

AIMS Mathematics, 2020
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R Ameri, Sárka Hoskova-Mayerova
exaly   +3 more sources

Hopf algebras for matroids over hyperfields [PDF]

Journal of Algebra, 2020
Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids. In this paper we generalize the notion of minors and direct sums from ordinary matroids to matroids over hyperfields.
Jaiung Jun, Matt Szczesny
exaly   +3 more sources

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Classification of Krasner Hyperfields of Order 4

Acta Mathematica Sinica, English Series, 2020
Let \(H\) be a non-empty set. A map from \(H\times H\) into the non-empty subsets of \(H\) is called a hyperoperation. The image of \((a,b)\) is denoted by \(ab\). Various notions generalize, one way or another, basic properties of groups. One such notion are polygroups. The authors study \(n\)-polygroups, where \(ab\) has at most \(n\) elements.
M Jafarpour, H Aghabozorgi
exaly   +3 more sources

Hyperfields and Random Sets

IFAC Postprint Volumes IPPV / International Federation of Automatic Control, 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
exaly   +2 more sources

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 ...
Christos G Massouros, Gerasimos G Massouros   +1 more
exaly   +3 more sources

On the hyperfields associated to valued fields

Journal of Pure and Applied Algebra
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. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields.
Alessandro Linzi, Pierre Touchard
exaly   +3 more sources

Theory of hyperrings and hyperfields

Algebra and Logic, 1985
The 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.
exaly   +3 more sources

Perfect matroids over skew hyperfields

European Journal of Combinatorics
Nathan Bowler, Rudi Pendavingh
exaly   +2 more sources

On the hyperfield or field-of-field concept

International Journal of Geographical Information Science, 2013
This article introduces the concept of hyperfield as a recursive field-of-field structure using a Unified Modelling Language UML modelling approach in two different variants, the hyperfield instance and hyperfield template models. The recursive property defines a hyperfield of degree n as a representation of a relation between n locations in ...
openaire   +1 more source

Hyperaffine planes over hyperfields

Journal of Geometry, 1995
The 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.
openaire   +2 more sources