Results 41 to 50 of about 394 (102)

On Real Hyperframes [PDF]

Journal of Hyperstructures
The purpose of this paper is to introduce and study hyperframes. Where a frame is a generlization of a basis of a vector space, a hyperframe will act as a generalization of a basis in hypervector space.
Cody Cassiday
doaj   +1 more source

Note on Isomorphism Theorems of Hyperrings

International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010
There are different notions of hyperrings (R, +, ·). In this paper, we extend the isomorphism theorems to hyperrings, where the additions and the multiplications are hyperoperations.
Muthusamy Velrajan, Arjunan Asokkumar, Heinz Gumm   +2 more
wiley   +1 more source

Perfect matroids over hyperfields

arXiv, 2019
19 ...
Bowler, Nathan, Pendavingh, Rudi A.
openaire   +3 more sources

Exact category of hypermodules

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
It is shown, among other things, that the category of hypermodules is an exact category, thus generalizing the classical case.
A. Madanshekaf
wiley   +1 more source

Commutative hypergroups associated with a hyperfield [PDF]

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2017
Let [Formula: see text] be a commutative hypergroup and [Formula: see text] a discrete commutative hypergroup. In this paper we introduce a commutative hypergroup [Formula: see text] associated with a hyperfield [Formula: see text] of [Formula: see text] based on [Formula: see text].
Heyer, Herbert, Kawakami, Satoshi, Tsurii, Tatsuya, Yamanaka, Satoe   +3 more
openaire   +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
openaire   +1 more source

New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker, Tong Jin, Oliver Lorscheid   +2 more
wiley   +1 more source

Tropical geometry over the tropical hyperfield

Rocky Mountain Journal of Mathematics, 2022
In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a nonarchimedean absolute value can be considered as a morphism into the tropical hyperfield.
openaire   +5 more sources

Hopf algebras for matroids over hyperfields [PDF]

, 2018
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 ...
Eppolito, Chris, Jun, Jaiung, Szczesny, Matt M.   +2 more
core  

A Note on Hypervector Spaces

, 2011
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence.
Roy, Sanjay, Samanta, T. K.
core   +1 more source