A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...

We study the connection between dimension of certain spaces harmonic functions on a group and its geometric algebraic properties. Our main result shows that (for sufficiently “nice” random walk measures) connected, compactly generated, locally compact has polynomial volume growth if only space linear finite dimension. This characterization is interesting in light fact Gromov’s theorem regarding...

The discipline of symbolic computation goes back to be beginnings of computers, as early on scientists carried out symbolic (exact) and algebraic manipulation of polynomials and quantified formulas on early computers. The theory of NP-completeness has exposed many of the investigated problems hard in the worst case. As it turned out in the 1980s, an exception is the problem of polynomial factor...

We give a new purely algebraic proof of the Baker-Campbell-Hausdorff theorem, which states that homogeneous components formal expansion $\log(e^Ae^B)$ are Lie polynomials. Our is based on recurrence formula for these and lemma if under certain conditions commutator non-commuting variable given polynomial polynomial, then itself polynomial.

To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...

In the last decade, algebraic and fast algebraic attacks are regarded as the most successful attacks on LFSR-based stream ciphers. Since the notion of algebraic immunity was introduced, the properties and constructions of Boolean functions with maximum algebraic immunity have been researched in a large number of papers. However, it is unclear whether these functions behave well against fast alg...