Results 11 to 20 of about 448 (100)

Recent results in hyperring and hyperfield theory

International Journal of Mathematics and Mathematical Sciences, 1988
This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the “sum” of two elements is a subset of the structure.
Anastase Nakassis
doaj   +2 more sources

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.
Thomas Vougiouklis, Souzana Vougiouklis
doaj   +2 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
exaly   +3 more sources

Root Selections and 2p-th Root Selections in Hyperfields

Discussiones Mathematicae - General Algebra and Applications, 2019
In this paper we define root selections and 2p-th root selections for hyperfields: these are multiplicative subgroups whose existence is equivalent to the existence of a well behaved square root function and 2p-th root function, respectively.
Gładki Paweł
doaj   +4 more sources

Advanced results in enumeration of hyperfields

AIMS Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Ameri, M. Eyvazi, S. Hoskova-Mayerova
exaly   +3 more sources

Hyper vector spaces over Krasner hyperfields [PDF]

Journal of Algebraic Hyperstructures and Logical Algebras, 2020
In this paper, we study hyper vector spaces over Krasner hyperfields. First, we introduce the notions of linearly independence (dependence) and basis for a hyper vector space. Second, we investigate their properties and prove some results for hyper vector spaces that are similar to that of vector spaces over fields.
M. Al-Tahan, Bijan Davvaz
exaly   +2 more sources

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.
Thomas Vougiouklis
doaj   +2 more sources

Quadratic structures associated to (multi)rings [PDF]

Categories and General Algebraic Structures with Applications, 2022
We consider certain pairs (A, T) where A is a (multi)ring andT ⊆ A is a multiplicative set that generates, by a convenient quotient construction,a (multi)structure that supports a quadratic form theory: withsome natural hypotheses we generalize ...
Kaique Roberto, Hugo Ribeiro, Hugo Mariano   +2 more
doaj   +1 more source

Matroids over hyperfields [PDF]

AIP Conference Proceedings, 2016
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. In fact, there are (at least) two natural notions of matroid in this context, which we call weak and strong matroids.
Baker, Matthew, Bowler, Nathan
openaire   +3 more sources

K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories [PDF]

Categories and General Algebraic Structures with Applications, 2022
We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]).
Kaique Roberto, Hugo Mariano
doaj   +1 more source