Generalized complex numbers over near-fields

Stefan Veldsman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The construction of the complex numbers over the reals has been generalized in many ways leading, amongs others, to the 2-dimensional elliptical complex numbers (= ordinary complex numbers), the parabolic complex numbers and the hyperbolic complex numbers. One can extend these to higher dimensions and also to using an arbitrary ring as the base ring. Here we propose a construction of generalized complex numbers over a near-field and investigate some of the structural properties of this near-ring.

Original languageEnglish
Pages (from-to)181-200
Number of pages20
JournalQuaestiones Mathematicae
Volume42
Issue number2
DOIs
Publication statusPublished - Feb 7 2019
Externally publishedYes

Keywords

  • complex near-ring
  • matrix near-ring
  • Near-ring
  • polynomial near-ring

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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