Displaying similar documents to “Notes on the algebra and geometry of polynomial representations.”

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.

Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller, Artur Korniłowicz (2016)

Formalized Mathematics

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In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.