Related papers: About special elements in quaternion algebras over…

We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$. However, a differential quaternion algebra need not be split over any…

{\small In this paper, we find a class of division quaternion algebras over the field }$\mathbb{Q}\left( i\right) ${\small \ and a class of division symbol algebras over a cyclotomic field.}

In this paper, we prove some relations between Fibonacci elements in an arbitrary algebra. Moreover, we define imaginary Fibonacci quaternions and imaginary Fibonacci octonions and we prove that always three arbitrary imaginary Fibonacci…

Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over the composite K of n quadratic number fields. Also, in Section 6, we obtain a characterization of…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…

We study well-rounded ideal lattices from totally definite quaternion algebras. We prove existence and classification results, and illustrate our methods with examples.

The purpose of the paper is to construct a new representation of dual quaternions called bi$-$periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual…

The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.

We present new classes of permutation polynomials over finite fields.

The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…

We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.

{\small In this paper we define and we study properties of} $\left(l,1,p+2q,q\cdot l\right) -$ {\small numbers,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small quaternions,} $\left(l,1,p+2q,q\cdot l\right) -$ {\small symbol elements. Finally,…

Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…

In this paper we define and study properties and applications of a, b, x0, x1 elements in some special cases.

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra…

In this paper, we introduce h(x)-Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K (K = R,C), which generalize both h(x)-Fibonacci quaternion polynomials and h(x)-Fibonacci octonion polynomials. For…

We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz…

Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in $\ell$-algebras, preferably in $f$-algebras, and in product algebras. The additional structure of an associative multiplication leads…