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Special Numbers, Special Quaternions and Special Symbol Elements

  • Diana Savin
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)

Abstract

Most mathematical notions have connections with real life. Although the theory of rings and algebras is abstract, however, this theory has many applications, some indirect, in real life. Many sets of real-life objects, taken together with one or more laws of composition, form algebraic structures with interesting properties. Quaternion algebras and of symbol algebras have applications in various branches of mathematics, but also in computer science, physics, signal theory. In this paper we define and we study properties of \(\left( l,1,p+2q,q\cdot l\right) -\) numbers, \(\left( l,1,p+2q,q\cdot l\right) -\) quaternions, \(\left( l,1,p+2q,q\cdot l\right) -\) symbol elements. Finally, we obtain an algebraic structure with these elements.

Keywords

Quaternion algebras; symbol algebras Fibonacci numbers Lucas numbers Fibonacci–Lucas quaternions Pell- Fibonacci–Lucas quaternions Open image in new window quaternions Open image in new window symbol elements 

2000 AMS Subject Classification

15A24 15A06 16G30 11R52 11B39 11R54 

Notes

Acknowledgements

The author dedicates this book chapter to her mother, Prof. Elena Savin.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceOvidius UniversityConstantaRomania

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