In this paper we investigate some results on the construction of irreducible polynomials over finite fields. Basic results on finite fields are introduced and proved. Several theorems proving irreducibility of certain polynomials over finite fields are presented and proved. Two theorems on the construction of special sequences of irreducible polynomials over finite fields are investigated in de...

In this work we study an abstract formulation of a problem posed by J.M. Dunn, T.J. Hagge et al. about the inclusion of varieties generated by the modular ortholattice of subspaces of C. We shall prove that, this abstract formulation is equivalent to the direct irreducibility for atomic complete modular ortholattices.

This paper surveys mathematical properties of (layered-) mixed matrices with emphasis on irreducibility and block-triangular decomposition. A matrix A is a mixed matrix if A = Q + T , where Q is a “constant” matrix and T is a “generic” matrix (or formal incidence matrix) in the sense that the nonzero entries of T are algebraically independent parameters. A layered mixed (or LM-) matrix is a mix...

Background: Although anterior shoulder dislocation is the most prevalent type of body dislocation, irreducible anterior shoulder dislocation is seldom reported in the literature, which is usually due to physical obstacles. Objectives: This study presents our findings regarding the causes of irreducibility of anterior shoulder dislocation associated with displaced fracture of the greater tuberos...

We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W -algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves. Dedicated to the 60th birthday of Professor Efim Zelmanov

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

In this paper we focus on tests and constructions of irreducible polynomials over nite elds. We revisit Rabin's (1980) algorithm providing a variant of it that improves Rabin's cost estimate by a log n factor. We give a precise analysis of the probability that a random polynomial of degree n contains no irreducible factors of degree less than O(log n). This probability is naturally related to B...

A criterion of irreducibility for induction products of evaluation modules of type A affine Hecke algebras is given. It is derived from multiplicative properties of the canonical basis of a quantum deformation of the Bernstein-Zelevinsky ring.