Advances in Applied Clifford Algebras

, Volume 25, Issue 4, pp 853–862 | Cite as

Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions

  • Cristina Flaut
  • Diana Savin


In this paper, we introduce the generalized Fibonacci–Lucas quaternions and we prove that the set of these elements is an order—in the sense of ring theory—of a quaternion algebra. Moreover, we investigate some properties of these elements.


Generalized quaternion algebra Fibonacci numbers Lucas numbers 

Mathematics Subject Classification

Primary 11R52 11B39 Secondary 16G30 15A06 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akyigit M., Kosal H., Tosun M.: Fibonacci generalized quaternions. Adv. Appl. Clifford Algebr. 24(3), 631–641 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Flaut, C., Savin, D.: Some properties of the symbol algebras of degree 3. Math. Reports 16(66)(3), 443–463 (2014)Google Scholar
  3. 3.
    Flaut C., Savin D., Iorgulescu G.: Some properties of Fibonacci and Lucas symbol elements. J. Math. Sci. Adv. Appl. 20, 37–43 (2013)Google Scholar
  4. 4.
    Flaut C., Shpakivskyi V.: On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions. Adv. Appl. Clifford Algebr. 23(3), 673–688 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Flaut C.: Some equations in algebras obtained by the Cayley-Dickson process. An. St. Univ. Ovidius Constanta 9(2), 45–68 (2001)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Horadam A.F.: A generalized Fibonacci sequence. Am. Math. Mon. 68, 455–459 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Horadam A.F.: Complex Fibonacci numbers and Fibonacci quaternions. Am. Math. Mon. 70, 289–291 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lam, T.Y.: Introduction to quadratic forms over fields. American Mathematical Society (2004)Google Scholar
  9. 9.
    Savin D.: About some split central simple algebras. An. St. Univ. Ovidius Constanta, Mat. Ser. 22(1), 263–272 (2014)MathSciNetGoogle Scholar
  10. 10.
    Voight, J.: The arithmetic of quaternion algebras. Available on the author’s website: (2015)
  11. 11.

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceOvidius UniversityConstantaRomania

Personalised recommendations