Related papers: On Canonical Subfield Preserving Polynomials

We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they…

Using the braided version of Lawvere's algebraic theories and Mac Lane's PROPs, we introduce polynomial identities for arbitrary algebraic structures in a braided monoidal category C as well as their codimensions in the case when C is…

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…

We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…

It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…

A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies…

Let $\mathbb{N}$ be the set of natural numbers. The Mac\'ias space $M(\mathbb{N})$ is the topological space $(\mathbb{N},\tau_M)$ where $\tau_M$ is generated by the collection of sets $\sigma_n := \{ m \in \mathbb{N} : \gcd(n, m) = 1 \}$.…

This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of…

We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…

We study the concept of hypervaluations on hyperfields. In particular, we show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of a hypervaluation onto an ordered abelian group (which…

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.

Hyperbolic polynomials are monic real-rooted polynomials. By Bronshtein's theorem, the increasingly ordered roots of a hyperbolic polynomial of degree $d$ with $C^{d-1,1}$ coefficients are locally Lipschitz and the solution map…

We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is…

A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are stably finite. In other words, given any field $K$ and any…

Given n polynomials in n variables of respective degrees d_1,...,d_n, and a set of monomials of cardinality d_1...d_n, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose…

We classify the $\mathscr{R}$-cross-sections of the monoid of order-preserving transformations on the $n$-element chain in terms of certain binary trees.

Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…

We find the minimal dimension for a truncated polynomial algebra over an arbitrary field for which there exists a "non-thin" subalgebra. Moreover, we discuss examples of subalgebras, and count them in low dimensions.

Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…