Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1141 |
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| author | Cristina Flaut Geanina Zaharia |
| author_facet | Cristina Flaut Geanina Zaharia |
| author_sort | Cristina Flaut |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T11:38:27Z |
| format | Article |
| id | doaj.art-aa562aafa70449718d72824121382a2a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:27Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aa562aafa70449718d72824121382a2a2023-11-30T23:37:45ZengMDPI AGMathematics2227-73902022-04-01107114110.3390/math10071141Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their ApplicationsCristina Flaut0Geanina Zaharia1Faculty of Mathematics and Computer Science, Ovidius University of Constanţa, Bd. Mamaia 124, 900527 Constanta, RomaniaDoctoral School of Mathematics, Ovidius University of Constanţa, 900527 Constanta, RomaniaDue 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.https://www.mdpi.com/2227-7390/10/7/1141Cayley–Dickson processalternative algebras |
| spellingShingle | Cristina Flaut Geanina Zaharia Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications Mathematics Cayley–Dickson process alternative algebras |
| title | Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications |
| title_full | Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications |
| title_fullStr | Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications |
| title_full_unstemmed | Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications |
| title_short | Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications |
| title_sort | remarks regarding computational aspects in algebras obtained by cayley dickson process and some of their applications |
| topic | Cayley–Dickson process alternative algebras |
| url | https://www.mdpi.com/2227-7390/10/7/1141 |
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