Research Article
BibTex RIS Cite

n-spaces

Year 2020, Volume: 69 Issue: 1, 431 - 440, 30.06.2020
https://doi.org/10.31801/cfsuasmas.668538

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.

References

  • 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.
  • Baker, C.A., Lane N.D. and Lorimer, J.W., A coordinatization for Moufang-Klingenberg Planes, Simon Stevin, 65 (1991), 3-22.
  • Bix, R., Octonion Planes over Local Rings, Trans. Amer. Math. Soc., 261(2) (1980), 417-438.
  • Blunck, A., Cross-ratios in Moufang-Klingenberg Planes, Geom. Dedicata, 43 (1992), 93-107.
  • 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.
  • Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970), 1-71.
  • Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., 2014.
  • Freudenthal, H., Octaven, Ausnahmegruppen, und Octavengeometrie. Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 49, 1951.
  • Jacobson, N., Structure and Representations of Jordan Algebras, Colloq. Publ. 39, Amer. Math. Soc., Providence, R.I., 1968.
  • Jordan, P., Über Eine Nicht-Desarguessche Ebene Projektive Geometrie. Abh. Math. Sem. Univ. Hamburg, 16 (1949), 74-76, . McCr : McCrimmon, K., The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras, Trans. of the Amer. Math. Soc., 139 (1969), 495-510, .
  • Springer, T.A., The Projective Octave Plane. Nederl. Akad. Wetensch. Proc. Ser. A, 63, Indag. Math., 22 (1960), 74-101.
Year 2020, Volume: 69 Issue: 1, 431 - 440, 30.06.2020
https://doi.org/10.31801/cfsuasmas.668538

Abstract

References

  • 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.
  • Baker, C.A., Lane N.D. and Lorimer, J.W., A coordinatization for Moufang-Klingenberg Planes, Simon Stevin, 65 (1991), 3-22.
  • Bix, R., Octonion Planes over Local Rings, Trans. Amer. Math. Soc., 261(2) (1980), 417-438.
  • Blunck, A., Cross-ratios in Moufang-Klingenberg Planes, Geom. Dedicata, 43 (1992), 93-107.
  • 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.
  • Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970), 1-71.
  • Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., 2014.
  • Freudenthal, H., Octaven, Ausnahmegruppen, und Octavengeometrie. Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 49, 1951.
  • Jacobson, N., Structure and Representations of Jordan Algebras, Colloq. Publ. 39, Amer. Math. Soc., Providence, R.I., 1968.
  • Jordan, P., Über Eine Nicht-Desarguessche Ebene Projektive Geometrie. Abh. Math. Sem. Univ. Hamburg, 16 (1949), 74-76, . McCr : McCrimmon, K., The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras, Trans. of the Amer. Math. Soc., 139 (1969), 495-510, .
  • Springer, T.A., The Projective Octave Plane. Nederl. Akad. Wetensch. Proc. Ser. A, 63, Indag. Math., 22 (1960), 74-101.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Atilla Akpınar 0000-0002-7612-2448

Publication Date June 30, 2020
Submission Date April 1, 2017
Acceptance Date December 23, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

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

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.