A three dimensional modification of the Gaussian number field

Year, pages: 2019, 63 - 76

For vectors in $\mathbf{E}₃$ we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications. \par Based on properties of hyperbolic (Clifford) complex numbers, we prove that the resulting algebra $\mathbb{T}$ is an associative algebra over a field and contains a subring isomorphic to hyperbolic complex numbers. Moreover, the algebra $\mathbb{T}$ is isomorphic to direct product $\mathbb{C}× \mathbb{R}$, and so it contains a subalgebra isomorphic to the Gaussian complex plane.

Haluška, J., Jastrzębska, M. 2019. A three dimensional modification of the Gaussian number field. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 63-76. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0020

Haluška, J., Jastrzębska, M. (2019). A three dimensional modification of the Gaussian number field. Tatra Mountains Mathematical Publications, 74(2), 63-76. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0020

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.