Polynomials over quaternions and coquaternions: a unified approach

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.(undefined)info:eu-repo/semantics/publishedVersio

On the roots of coquaternions

In this paper we give a complete characterization of the nth roots of a coquaternion q. In particular, we show that the number and type of roots-isolated and/or hyperboloidal-depend on the nature of q, on the parity of n and (eventually) on the sign of the real part of q. We also show how the coquaternionic formalism can be used to obtain, in a simple manner, explicit expressions for the real nth roots of any 2 x 2 real matrix.Research at CMAT was financed by Portuguese Funds through FCT - Fundacao para a Ciencia 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 (Fundacao para a Ciencia 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.info:eu-repo/semantics/publishedVersio