Displaying similar documents to “Some Algebraic Properties of Polynomial Rings”

On Roots of Polynomials and Algebraically Closed Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

On the dynamics of extendable polynomial endomorphisms of ℝ²

Ewa Ligocka (2007)

Annales Polonici Mathematici

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We extend the results obtained in our previous paper, concerning quasiregular polynomials of algebraic degree two, to the case of polynomial endomorphisms of ℝ² whose algebraic degree is equal to their topological degree. We also deal with some other classes of polynomial endomorphisms extendable to ℂℙ².

Local polynomials are polynomials

C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)

Studia Mathematica

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We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.

Reciprocal Stern Polynomials

A. Schinzel (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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A partial answer is given to a problem of Ulas (2011), asking when the nth Stern polynomial is reciprocal.

Plane Jacobian conjecture for simple polynomials

Nguyen Van Chau (2008)

Annales Polonici Mathematici

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A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.