Research Article

n-spaces

Volume: 69 Number: 1 June 30, 2020
EN

n-spaces

Abstract

In this paper, we introduce n-spaces constructed over an local ring with the maximal ideal (of non-unit elements). So, we give the example of an octonion n-space. Finally, we give two collineations of quaternion n-space.

Keywords

References

  1. Akpinar, A. and Erdogan, F.O., Dual Quaternionic (n-1)-Spaces Defined by Special Jordan Algebras of Dimension 4n²-2n, JP Journal of Geometry and Topology, 21(4) (2018), 327-364.
  2. Baker, C.A., Lane N.D. and Lorimer, J.W., A coordinatization for Moufang-Klingenberg Planes, Simon Stevin, 65 (1991), 3-22.
  3. Bix, R., Octonion Planes over Local Rings, Trans. Amer. Math. Soc., 261(2) (1980), 417-438.
  4. Blunck, A., Cross-ratios in Moufang-Klingenberg Planes, Geom. Dedicata, 43 (1992), 93-107.
  5. Celik, B., Akpinar, A. and Ciftci, S., 4-Transitivity and 6-figures in some Moufang-Klingenberg planes, Monatshefte für Mathematik, 152(4) (2007), 283-294.
  6. Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970), 1-71.
  7. Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., 2014.
  8. Freudenthal, H., Octaven, Ausnahmegruppen, und Octavengeometrie. Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 49, 1951.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 30, 2020

Submission Date

April 1, 2017

Acceptance Date

December 23, 2019

Published in Issue

Year 2020 Volume: 69 Number: 1

APA
Akpınar, A. (2020). n-spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 431-440. https://doi.org/10.31801/cfsuasmas.668538
AMA
1.Akpınar A. n-spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):431-440. doi:10.31801/cfsuasmas.668538
Chicago
Akpınar, Atilla. 2020. “N-spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (1): 431-40. https://doi.org/10.31801/cfsuasmas.668538.
EndNote
Akpınar A (June 1, 2020) n-spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 431–440.
IEEE
[1]A. Akpınar, “n-spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 431–440, June 2020, doi: 10.31801/cfsuasmas.668538.
ISNAD
Akpınar, Atilla. “N-spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 1, 2020): 431-440. https://doi.org/10.31801/cfsuasmas.668538.
JAMA
1.Akpınar A. n-spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:431–440.
MLA
Akpınar, Atilla. “N-spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, June 2020, pp. 431-40, doi:10.31801/cfsuasmas.668538.
Vancouver
1.Atilla Akpınar. n-spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020 Jun. 1;69(1):431-40. doi:10.31801/cfsuasmas.668538