<abstract xmlns="http://www.w3.org/1999/xhtml">For vectors in <bold>E</bold>3 we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications.Based on properties of hyperbolic (Clifford) complex numbers, we prove that the resulting algebra 𝕋 is an associative algebra over a field and contains a subring isomorphic to hyperbolic complex numbers. Moreover, the algebra 𝕋 is isomorphic to direct product ℂ<italic>×</italic>ℝ, and so it contains a subalgebra isomorphic to the Gaussian complex plane.</abstract>

For vectors in E3 we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications.Based on properties of hyperbolic (Clifford) complex numbers, we prove that the resulting algebra 𝕋 is an associative algebra over a field and contains a subring isomorphic to hyperbolic complex numbers. Moreover, the algebra 𝕋 is isomorphic to direct product ℂ×ℝ, and so it contains a subalgebra isomorphic to the Gaussian complex plane.

A Three Dimensional Modification of the Gaussian Number Field

Siedlce University of Natural Sciences and Humanities

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Three Dimensional Modification of the Gaussian Number Field"}

For vectors in E3 we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and...

A Three Dimensional Modification of the Gaussian Number Field

Publié en ligne: 15 nov. 2019

Pages: 63 - 76

Reçu: 03 oct. 2019

DOI: https://doi.org/10.2478/tmmp-2019-0020

Mots clés
Normed field, three dimensions, factor ring, generalized complex numbers

© 2019 Ján Haluška et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Three Dimensional Modification of the Gaussian Number Field

Publié en ligne: 15 nov. 2019

Pages: 63 - 76

Reçu: 03 oct. 2019

DOI: https://doi.org/10.2478/tmmp-2019-0020

Mots clésNormed field, three dimensions, factor ring, generalized complex numbers

© 2019 Ján Haluška et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Normed field, three dimensions, factor ring, generalized complex numbers