Related papers: About special elements in quaternion algebras over…
In this paper we provide some properties of k-potent elements in algebras obtained by the Cayley-Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for…
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…
In this paper, we define the incomplete h(x)-Fibonacci and h(x)-Lucas polynomials, we study recurrence relations and some properties of these polynomials
This work proposes two nodal type nonconforming finite elements over convex quadrilaterals, which are parts of a finite element exact sequence. Both elements are of 12 degrees of freedom (DoFs) with polynomial shape function spaces…
Let $\mathcal{H}^{a,b}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to investigate super-biderivations and local superderivations on the generalized quaternion algebra, which is viewed as a class…
Let $F=\mathbb{F}_q(T)$ be the field of rational functions with $\mathbb{F}_q$-coefficients, and $A=\mathbb{F}_q[T]$ be the subring of polynomials. Let $D$ be a division quaternion algebra over $F$ which is split at $1/T$. Given an…
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.
Starting from known results, due to Y. Tian in [Ti; 00], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right real matrix representations for the complex quaternions and…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were…
We generalize the $\Lambda$-adic Shintani lifting for $GL_2(Q)$ to indefinite quaternion algebras over $Q$.
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…