Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Cristina Flaut and Geanina Zaharia
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Cristina Flaut: Faculty of Mathematics and Computer Science, Ovidius University of Constanţa, Bd. Mamaia 124, 900527 Constanta, Romania
Geanina Zaharia: Doctoral School of Mathematics, Ovidius University of Constanţa, 900527 Constanta, Romania

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: Due to the computational aspects which appear in the study of algebras obtained by the Cayley–Dickson process, it is difficult to obtain nice properties for these algebras. For this reason, finding some identities in such algebras plays an important role in obtaining new properties of these algebras and facilitates computations. In this regard, in the first part of this paper, we present some new identities and properties in algebras obtained by the Cayley–Dickson process. As another remark regarding the computational aspects in these algebras, in the last part of this paper, we solve some quadratic equations in the real division quaternion algebra when their coefficients are some special elements. These special coefficients allowed us to solve interesting quadratic equations, providing solutions directly, without using specialized softs.

Keywords: Cayley–Dickson process; alternative algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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