{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T21:35:28Z","timestamp":1771018528736,"version":"3.50.1"},"reference-count":0,"publisher":"Wiley","issue":"37","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["F-510\/3\/DSA\/98(SAP-I)"],"award-info":[{"award-number":["F-510\/3\/DSA\/98(SAP-I)"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>Let <jats:italic>R<\/jats:italic> be a ring and <jats:italic>S<\/jats:italic> a nonempty subset of <jats:italic>R<\/jats:italic>. Suppose that <jats:italic>\u03b8<\/jats:italic> and <jats:italic>\u03d5<\/jats:italic> are endomorphisms of <jats:italic>R<\/jats:italic>. An additive mapping <jats:italic>\u03b4<\/jats:italic> : <jats:italic>R<\/jats:italic> \u2192 <jats:italic>R<\/jats:italic> is called a left (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivation (resp., Jordan left (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010derivation) on <jats:italic>S<\/jats:italic> if <jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic><jats:italic>y<\/jats:italic>) = <jats:italic>\u03b8<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>\u03b4<\/jats:italic>(<jats:italic>y<\/jats:italic>) + <jats:italic>\u03d5<\/jats:italic>(<jats:italic>y<\/jats:italic>)<jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic>) (resp., <jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup>) = <jats:italic>\u03b8<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic>) + <jats:italic>\u03d5<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic>)) holds for all <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic> \u2208 <jats:italic>S<\/jats:italic>. Suppose that <jats:italic>J<\/jats:italic> is a Jordan ideal and a subring of a 2\u2010torsion\u2010free prime ring <jats:italic>R<\/jats:italic>. In the present paper, it is shown that if <jats:italic>\u03b8<\/jats:italic> is an automorphism of <jats:italic>R<\/jats:italic> such that <jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup>) = 2<jats:italic>\u03b8<\/jats:italic>(<jats:italic>x<\/jats:italic>)<jats:italic>\u03b4<\/jats:italic>(<jats:italic>x<\/jats:italic>) holds for all <jats:italic>x<\/jats:italic> \u2208 <jats:italic>J<\/jats:italic>, then either <jats:italic>J<\/jats:italic>\u2ac5<jats:italic>Z<\/jats:italic>(<jats:italic>R<\/jats:italic>) or <jats:italic>\u03b4<\/jats:italic>(<jats:italic>J<\/jats:italic>) = (0). Further, a study of left (<jats:italic>\u03b8<\/jats:italic>, <jats:italic>\u03b8<\/jats:italic>)\u2010derivations of a prime ring <jats:italic>R<\/jats:italic> has been made which acts either as a homomorphism or as an antihomomorphism of the ring <jats:italic>R<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/s0161171204309075","type":"journal-article","created":{"date-parts":[[2004,8,5]],"date-time":"2004-08-05T13:38:35Z","timestamp":1091713115000},"page":"1957-1964","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["On Jordan ideals and left (<i>\u03b8<\/i>, <i>\u03b8<\/i>)\u2010derivations in prime rings"],"prefix":"10.1155","volume":"2004","author":[{"given":"S. M. A.","family":"Zaidi","sequence":"first","affiliation":[]},{"given":"Mohammad","family":"Ashraf","sequence":"additional","affiliation":[]},{"given":"Shakir","family":"Ali","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,8,5]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/296847.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204309075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T21:08:07Z","timestamp":1723064887000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204309075"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"37","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204309075"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204309075","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-09-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-08-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}