Related papers: Division properties of commuting polynomials
Let $\mathbb{F}$ be a finite field and let $f$ be a linear polynomial in $\mathbb{F}[x]$. We investigate the number of polynomials of degree $d$ which commute with $f$ under composition. In so doing, we rediscover a result of Park, but with…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We consider properties of polynomials with coefficients in division rings. A theorem on the decomposition of a polynomial with coefficients in an arbitrary division ring is obtained. It is shown that if a non-central element is not a root…
In this paper I consider polynomial composites with the coefficients from $K\subset L$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…
Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational…
In this paper, we gave some properties of binomial coefficient.
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic…
We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.
We address some questions concerning indecomposable polynomials and their spectrum. How does the spectrum behave via reduction or specialization, or via a more general ring morphism? Are the indecomposability properties equivalent over a…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.