Natalio H. Guersenzvaig

most citedA Closed Formula for the Product in Simple Integral Extensions

4 citations · 6 across the 3 of their papers we have counts for

collaborators

6 papers

math.RA2013

Roots multiplicity and square-free factorization of polynomials using companion matrices

Natalio H. Guersenzvaig, Fernando Szechtman

Given an arbitrary monic polynomial $f$ over a field $F$ of characteristic 0, we use companion matrices to construct a polynomial $M_{f} \in F [X]$ of minimum degree such that for each…

math.RA2013★ 2 cited

Generalized Artin-Schreier polynomials

Natalio H. Guersenzvaig, Fernando Szechtman

Let $F$ be a field of prime characteristic $p$ containing $F_{p^{n}}$ as a subfield. We refer to $q (X) = X^{p^{n}} - X - a \in F [X]$ as a generalized Artin-Schreier polynomial. Suppose that $…

math.RA2013

Is every matrix similar to a polynomial in a companion matrix?

Natalio H. Guersenzvaig, Fernando Szechtman

Given a field $F$ , an integer $n \geq 1$ , and a matrix $A \in M_{n} (F)$ , are there polynomials $f, g \in F [X]$ , with $f$ monic of degree $n$ , such that $A$ is similar to $g (C_{f})$ , where…

math.RA2013

Elementary criteria for irreducibility of $f (X^{n})$

Natalio H. Guersenzvaig

Very simple sufficient conditions for the irreducibility of $f (X^{n})$ over an arbitrary unique factorization domain $Z$ are established via a generalization of a well known theorem…

math.RA2010★ 4 cited

A Closed Formula for the Product in Simple Integral Extensions

Natalio H. Guersenzvaig, Fernando Szechtman

Let $ξ$ be an algebraic number and let $α, β \in Q [ξ]$ . An explicit formula for the coordinates of the product $α β$ is given in terms of the coordinates of $α$ and $β$ and th…

math.RA2010

Subalgebras of Matrix Algebras Generated by Companion Matrices

Natalio H. Guersenzvaig, Fernando Szechtman

Let $f, g \in Z [X]$ be monic polynomials of degree $n$ and let $C, D \in M_{n} (Z)$ be the corresponding companion matrices. We find necessary and sufficient conditions for the subalgebra…

Roots multiplicity and square-free factorization of polynomials using companion matrices

Generalized Artin-Schreier polynomials

Is every matrix similar to a polynomial in a companion matrix?

Elementary criteria for irreducibility of f(Xn)

A Closed Formula for the Product in Simple Integral Extensions

Subalgebras of Matrix Algebras Generated by Companion Matrices

Elementary criteria for irreducibility of $f (X^{n})$