{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:26:39Z","timestamp":1760145999913,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T00:00:00Z","timestamp":1727395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP2\/293\/45"],"award-info":[{"award-number":["RGP2\/293\/45"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the relationship between the commutativity of rings and the properties of their multiplicative generalized derivations. Let F be a ring with a semiprime ideal \u03a0. A map \u03d5:F\u2192F is classified as a multiplicative generalized derivation if there exists a map \u03c3:F\u2192F such that \u03d5(xy)=\u03d5(x)y+x\u03c3(y) for all x,y\u2208F. This study focuses on semiprime ideals \u03a0 that admit multiplicative generalized derivations \u03d5 and G that satisfy certain differential identities within F. By examining these conditions, the paper aims to provide new insights into the structural aspects of rings, particularly their commutativity in relation to the behavior of such derivations.<\/jats:p>","DOI":"10.3390\/axioms13100669","type":"journal-article","created":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T07:49:24Z","timestamp":1727423364000},"page":"669","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Identities Related to Semiprime Ideal of Rings with Multiplicative Generalized Derivations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9570-4714","authenticated-orcid":false,"given":"Ali Yahya","family":"Hummdi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 61471, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8328-4293","authenticated-orcid":false,"given":"Emine Ko\u00e7","family":"S\u00f6g\u00fctc\u00fc","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Sivas Cumhuriyet University, Sivas 58140, Turkey"}]},{"given":"\u00d6znur","family":"G\u00f6lba\u015f\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Sivas Cumhuriyet University, Sivas 58140, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3955-7941","authenticated-orcid":false,"given":"Nadeem ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1090\/S0002-9939-1957-0095863-0","article-title":"Derivations in prime rings","volume":"8","author":"Posner","year":"1957","journal-title":"Proc. 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