Partial orders on \(C = D + Di\) and \(H = D + Di + Dj + Dk\)

  • Authors

    • Jingjing Ma Department of Mathematics, School of Science and Computer Engineering, University of Houston-Clear Lake, USA
    2015-10-10
    https://doi.org/10.14419/ijams.v3i2.4773
  • Complex number, Directed partial order, Lattice order, Partial order, Quaternion.

  • Abstract

    Let \(D\) be a totally ordered integral domain. We study partial orders on the rings \(C = D + Di\) and \(H = D + Di + Dj + Dk\), where \(i^{2} = j^{2} = k^{2} = -1\).

  • References

    1. [1] G. Birkho, R. S. Pierce, Lattice-ordered rings, An. Acad. Brasil. Ci., 28 (1956), 41-69.

      [2] L. Fuchs, Partially ordered algebraic systems, Dover Publications, Inc., (1963).

      [3] J. Ma, Lecture notes on algebraic structure of lattice-ordered rings, World Scientific Publishing, (2014).

      [4] J. Ma, Directed partial orders on real quaternions, Quaestiones Mathematicae, (to appear).

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  • How to Cite

    Ma, J. (2015). Partial orders on \(C = D + Di\) and \(H = D + Di + Dj + Dk\). International Journal of Advanced Mathematical Sciences, 3(2), 156-160. https://doi.org/10.14419/ijams.v3i2.4773