Homotopes of Quasi-Jordan Algebras
The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/11/1045 |
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| author | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom |
| author_facet | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom |
| author_sort | Reem K. Alhefthi |
| collection | DOAJ |
| description | The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if it is isomorphic to a quasi-Jordan subalgebra of some dialgebras. Keeping in view the pivotal role of homotopes in the theory of Jordan algebras, we begin a study of the homotopes of quasi-Jordan algebras; among other related results, we show that the homotopes of any special quasi-Jordan algebra are special quasi-Jordan algebras and that the homotopes of a K-B quasi-Jordan algebra is a quasi-Jordan algebra. In the sequel, we also give some open problems. |
| first_indexed | 2024-03-09T17:01:15Z |
| format | Article |
| id | doaj.art-174cad8c48744e38b207d88908421887 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:01:15Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-174cad8c48744e38b207d889084218872023-11-24T14:28:59ZengMDPI AGAxioms2075-16802023-11-011211104510.3390/axioms12111045Homotopes of Quasi-Jordan AlgebrasReem K. Alhefthi0Akhlaq A. Siddiqui1Fatmah B. Jamjoom2Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaMathematics Departments, College of Sciences, King Abdul Aziz University, P.O. Box 80200, Jeddah 21589, Saudi ArabiaThe notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if it is isomorphic to a quasi-Jordan subalgebra of some dialgebras. Keeping in view the pivotal role of homotopes in the theory of Jordan algebras, we begin a study of the homotopes of quasi-Jordan algebras; among other related results, we show that the homotopes of any special quasi-Jordan algebra are special quasi-Jordan algebras and that the homotopes of a K-B quasi-Jordan algebra is a quasi-Jordan algebra. In the sequel, we also give some open problems.https://www.mdpi.com/2075-1680/12/11/1045Jordan algebradialgebraquasi-Jordan algebrazero partsplit quasi-Jordan algebra |
| spellingShingle | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom Homotopes of Quasi-Jordan Algebras Axioms Jordan algebra dialgebra quasi-Jordan algebra zero part split quasi-Jordan algebra |
| title | Homotopes of Quasi-Jordan Algebras |
| title_full | Homotopes of Quasi-Jordan Algebras |
| title_fullStr | Homotopes of Quasi-Jordan Algebras |
| title_full_unstemmed | Homotopes of Quasi-Jordan Algebras |
| title_short | Homotopes of Quasi-Jordan Algebras |
| title_sort | homotopes of quasi jordan algebras |
| topic | Jordan algebra dialgebra quasi-Jordan algebra zero part split quasi-Jordan algebra |
| url | https://www.mdpi.com/2075-1680/12/11/1045 |
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