{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:20Z","timestamp":1760150300220,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T00:00:00Z","timestamp":1699574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms12111045","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T02:02:42Z","timestamp":1699840962000},"page":"1045","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Homotopes of Quasi-Jordan Algebras"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9344-2008","authenticated-orcid":false,"given":"Reem K.","family":"Alhefthi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0021-0847","authenticated-orcid":false,"given":"Akhlaq A.","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5596-1050","authenticated-orcid":false,"given":"Fatmah B.","family":"Jamjoom","sequence":"additional","affiliation":[{"name":"Mathematics Departments, College of Sciences, King Abdul Aziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jacobson, N. (1968). 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