In this paper are characterized the polynomials, in terms of their coefficients, that have all their orbits dense in the set of 3-adic integers Z3.

A sequence u over a nite eld Fq is called an (f(x); m)-interleaved sequence 1] if f(x) is a common characteristic polynomial of all its m-decimated sequences. This paper demonstrate how the subjects such as the minimal polynomial, the linear span, the period and the correlation values of an (f(x); m)-interleaved sequence are related to its m-decimated sequences when f(x) is irreducible, and mak...

Definition. An algebraic integer is the root of a monic polynomial in Z[x]. An algebraic number is the root of any non-zero polynomial in Z[x]. We are interested in studying the structure of the ring of algebraic integers in an algebraic number field. A number field is a finite extension of Q. We’ll assume that the number fields we consider are all subfields of C. Definition. Suppose that K and...

Let F be an algebraically closed field of characteristic p > 0 and G be a quasi-simple group with G/Z(G) ∼= An. We describe the minimal polynomials of elements of order p in irreducible representations of G over F . If p = 2 we determine the minimal polynomials of elements of order 4 in 2modular irreducible representations of An, Sn, 3 ·A6, 3 ·S6, 3 ·A7, and 3 ·S7.

The beta-conjugates of a base of numeration β > 1, β being a Parry number, were introduced by Boyd, in the context of the Rényi-Parry dynamics of numeration system and the beta-transformation. These beta-conjugates are canonically associated with β. Let β > 1 be a real algebraic number. A more general definition of the beta-conjugates of β is introduced in terms of the Parry Upper function fβ(z...

A polynomial f(t) in an Ore extension K[t;S,D] over a division ring K is a Wedderburn polynomial if f(t) is monic and is the minimal polynomial of an algebraic subset of K. These polynomials have been studied in [LL5]. In this paper, we continue this study and give some applications to triangulation, diagonalization and eigenvalues of matrices over a division ring in the general setting of (S,D...