Results 11 to 20 of about 239 (103)

Root Selections and 2p-th Root Selections in Hyperfields [PDF]

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   +6 more sources

Geometry of tropical extensions of hyperfields [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics
We study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed.
James Maxwell, Ben Smith
core   +8 more sources

Geometry of hyperfields

Journal of Algebra, 2021
26 pages, Final version to appear in Journal of ...
Jaiung Jun
exaly   +3 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

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, Matt Szczesny
exaly   +3 more sources

A Result of Krasner in Categorial Form [PDF]

Mathematics, 2023
In 1957, M. Krasner described a complete valued field (K,v) as the inverse limit of a system of certain structures, called hyperfields, associated with (K,v).
Alessandro Linzi
doaj   +2 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

Hyperfield Grassmannians

Advances in Mathematics, 2019
31 pages.
Anderson, Laura, Davis, James F.
openaire   +5 more sources

Perfect matroids over hyperfields [PDF]

arXiv, 2019
19 ...
Bowler, Nathan, Pendavingh, Rudi A.
openaire   +5 more sources