Related papers: Extensions of Hyperfields
We determine all isomorphism classes of hyperfields of a given finite order which can be obtained as quotients of finite fields of sufficiently large order. Using this result, we determine which hyperfields of order at most 4 are quotients…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…
We construct a class of finite rank multiplicative subgroups of the complex numbers such that the expansion of the real field by such a group is model-theoretically well-behaved. As an application we show that a classification of expansions…
The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…
We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
We study mixed multiquadratic field extensions as splitting fields for central simple algebras of exponent $2$ in characteristic $2$. As an application, we provide examples of nonexcellent mixed biquadratic field extensions.
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)…
Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method…
In this paper we investigate the possible supersymmetric extensions for the massive (bi)gravity theories in the lowest non-trivial order. For this purpose we construct the cubic interaction vertices for massive spin-2 and one or two massive…
We study the behaviour of forking in valued fields, and we give several sufficient conditions for parameter sets in a Henselian valued field of residue characteristic zero to be an extension base. Notably, we consider arbitrary (potentially…
For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a consequence, we obtain a local uniformization theorem for…
We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we…
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…