We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a ...

Let Fq seja o corpo finito com q elementos, p = char Fq. O grupo GL2 (Fq) atua naturalmente no conjunto de polinômios irredutíveis acima de Fq de grau pelo menos 2. Neste trabalho estamos interessados na caracterização ...

Let $\mathbb {F}_{q} $ be a finite field with $ q $ elements. In this thesis, we focus on two types of problems about irreducible polynomials. The first one is the construction of irreducible polynomials from the composition ...

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the ...

The objective of this work is to study the factorization in irreducible factors of (...) over (...), where q denotes the power of a prime p, (...) is a finite field with q elements and (...) is a Dickson polynomial of the ...

The objective of this work is, study minimal cyclic codes viewed as ideals of a group algebra FqG, where Fq is a finite field q elements and G a finite cyclic group of order n. Imposing conditions at n and q, we determined ...

Let n be a positive integer and let F_{q^n} be the finite field with q^n elements, where q is a prime power. The aim of this work is to study a natural action of the Projective Semilinear Group PΓL(2,q^n) = PGL(2,q^n)xGa ...

Let (...) be a subgroup of (...). Let F be a subfield of C, the field of complex numbers. The field F is called a spliting field for (...) if (...) is conjugate in (...) to a subgroup in (...). The main result of this work ...