Polynomials over Quaternions and Coquaternions: A Unified Approach

  • Maria Irene Falcão
  • Fernando Miranda
  • Ricardo Severino
  • Maria Joana SoaresEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)


This paper aims to present, in a unified manner, results which are valid on both the algebras of quaternions and coquaternions and, simultaneously, call the attention to the main differences between these two algebras. The rings of one-sided polynomials over each of these algebras are studied and some important differences in what concerns the structure of the set of their zeros are remarked. Examples illustrating this different behavior of the zero-sets of quaternionic and coquaternionic polynomials are also presented.


Quaternions Coquaternions Polynomials Zeros 



Research at CMAT was financed by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s (Fundação para a Ciência e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on “Competitiveness and Internationalization - COMPETE 2020” under the PT2020 Partnership Agreement.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Maria Irene Falcão
    • 1
  • Fernando Miranda
    • 1
  • Ricardo Severino
    • 2
  • Maria Joana Soares
    • 3
    Email author
  1. 1.CMAT and Departamento de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal
  2. 2.Departamento de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal
  3. 3.NIPE and Departamento de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal

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