Results 61 to 70 of about 112 (84)

Hyperhomographies on Krasner Hyperfields [PDF]

Symmetry, 2019
In this paper, we introduce generalized homographic transformations as hyperhomographies over Krasner hyperfields.These particular algebraic hyperstructues are quotient structures of classical fields modulo normal groups. Besides, we define some hyperoperations and investigate the properties of the derived hypergroups and H v -groups associated ...
Irina Cristea, Morteza Jafarpour, Vahid Vahedi   +2 more
exaly   +2 more sources

Hyperfields, truncated DVRs, and valued fields [PDF]

Journal of Number Theory, 2020
For any two complete discrete valued fields $K_1$ and $K_2$ of mixed characteristic with perfect residue fields, we show that if the $n$-th valued hyperfields of $K_1$ and $K_2$ are isomorphic over $p$ for each $n\ge1$, then $K_1$ and $K_2$ are isomorphic.
Junguk Lee
exaly   +4 more sources

Advanced results in enumeration of hyperfields

AIMS Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reza Ameri
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
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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.
Hossien Aghabozorgi, Morteza Jafarpour
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 Massouros, Gerasimos 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
Rudi Pendavingh, Nathan Bowler
exaly   +2 more sources