{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T17:18:04Z","timestamp":1772990284591,"version":"3.50.1"},"reference-count":25,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T00:00:00Z","timestamp":1743379200000},"content-version":"vor","delay-in-days":89,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    A well\u2010known result by Upmeier states that every derivation on a universally reversible JC\u2010algebra\n                    <jats:italic>A<\/jats:italic>\n                    \u2286\n                    <jats:italic>B<\/jats:italic>\n                    (\n                    <jats:italic>H<\/jats:italic>\n                    )\n                    <jats:sub>sa<\/jats:sub>\n                    extends to the C\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010algebra [\n                    <jats:italic>A<\/jats:italic>\n                    ] generated by\n                    <jats:italic>A<\/jats:italic>\n                    in\n                    <jats:italic>B<\/jats:italic>\n                    (\n                    <jats:italic>H<\/jats:italic>\n                    ). In this paper, we significantly strengthen this result by proving that every Jordan derivation on a universally reversible JC\u2010algebra\n                    <jats:italic>A<\/jats:italic>\n                    extends to \u2009\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010derivations on its universal enveloping real and complex C\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010algebras\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) and\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ), respectively. Since every C\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010algebra generated by A is a quotient of its universal enveloping C\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010algebra\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ),  Upmeier\u2019s result follows as a direct corollary of our findings. Moreover, this work sheds new light on the deep structural relationship between JC\u2010algebras and their universal enveloping algebras, further enriching the understanding of their interplay. The proofs are rooted in the decomposition\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) =\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) \u2295\n                    <jats:italic>i<\/jats:italic>\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ), where\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) = {\n                    <jats:italic>x<\/jats:italic>\n                    \u2208\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) : \u03a6\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ) =\n                    <jats:italic>x<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    } and \u03a6\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    is the unique \u2009\n                    <jats:sup>\u2217<\/jats:sup>\n                    \u2010antiautomorphism of\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sup>\u2217<\/jats:sup>\n                    (\n                    <jats:italic>A<\/jats:italic>\n                    ) of order 2 that fixes the points of\n                    <jats:italic>A<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1155\/ijmm\/6654980","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T08:10:23Z","timestamp":1743408623000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Derivations and Extensions in JC\u2010Algebras"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5596-1050","authenticated-orcid":false,"given":"Fatmah B.","family":"Jamjoom","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Doha A.","family":"Abulhamail","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,3,31]]},"reference":[{"key":"e_1_2_10_1_2","first-page":"79","article-title":"On Derivations on Rings and Their Applications","volume":"25","author":"Ashraf M.","year":"2006","journal-title":"The Aligarh Bulletin Of Mathematics"},{"key":"e_1_2_10_2_2","first-page":"1786","article-title":"Chi-Square Distribution: New Derivations and Environmental Application","volume":"7","author":"Senkow T. 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Extensions of Derivations on JC-Algebras 2023 https:\/\/doi.org\/10.20944\/preprints202311.1982.v1.","DOI":"10.20944\/preprints202311.1982.v1"},{"key":"e_1_2_10_23_2","volume-title":"Notes on Real and Complex C\u2217-algebras","author":"Goodearl K.","year":"1982"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-11867"},{"key":"e_1_2_10_25_2","unstructured":"AbulhamailD. A. On Recent Preserve Problem 2022 Department of Mathematics Kind Abdulaziz University PhD thesis."}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/6654980","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/ijmm\/6654980","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/6654980","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T12:18:28Z","timestamp":1772972308000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/ijmm\/6654980"}},"subtitle":[],"editor":[{"given":"Armando","family":"S\u00e1nchez-Nungaray","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/ijmm\/6654980"],"URL":"https:\/\/doi.org\/10.1155\/ijmm\/6654980","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-10-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-07","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-31","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6654980"}}