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Keywords = split quasi-Jordan algebra

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16 pages, 306 KB  
Article
Homotopes of Quasi-Jordan Algebras
by Reem K. Alhefthi, Akhlaq A. Siddiqui and Fatmah B. Jamjoom
Axioms 2023, 12(11), 1045; https://doi.org/10.3390/axioms12111045 - 10 Nov 2023
Cited by 1 | Viewed by 1404
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Algebra and Number Theory)
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