### On the Eigenvalues of some Class of Pseudo-linear Transformations

Milica Anđelić (2007)

Publications de l'Institut Mathématique

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Milica Anđelić (2007)

Publications de l'Institut Mathématique

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Franz Halter-Koch (1993)

Rendiconti del Seminario Matematico della Università di Padova

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Shigeki Akiyama, Toufik Zaimi (2013)

Open Mathematics

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A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one,...

Nahay, John Michael (2004)

International Journal of Mathematics and Mathematical Sciences

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Piotr Jędrzejewicz (2008)

Open Mathematics

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Let k be a field, let $$G$$ be a finite group. We describe linear $$G$$ -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

Toufik Zaïmi (2011)

Publications de l'Institut Mathématique

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De Filippis, V., Di Vincenzo, O.M. (2001)

Mathematica Pannonica

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Handelman, David (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Piotr Jędrzejewicz (2013)

Open Mathematics

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We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.

Levin, Alexander B. (2001)

International Journal of Mathematics and Mathematical Sciences

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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.

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.