{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:19:44Z","timestamp":1773515984839,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"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>In this note, we will examine the relationship between a generalized derivation \u03dd associated with a derivation \u2202 that satisfies specific algebraic identities and the behavior of a factor ring S\/P, where P is a prime ideal of any ring S. We will also explore several consequences and special cases as applications of our findings. Additionally, various examples have been provided to highlight the necessity of the primeness hypothesis in our theorems.<\/jats:p>","DOI":"10.3390\/axioms14040247","type":"journal-article","created":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T05:35:03Z","timestamp":1742880903000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Prime Ideals in Rings Satisfying Certain Functional Identities"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2723-446X","authenticated-orcid":false,"given":"Kholood","family":"Alnefaie","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Madinah 42353, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5334-6169","authenticated-orcid":false,"given":"Radwan M.","family":"Al-omary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ibb University, Ibb 70270, Yemen"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"ref_1","first-page":"179","article-title":"Reduced rings, Morita contexts and derivations","volume":"10","author":"Nauman","year":"2008","journal-title":"East-West J. 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Action of prime ideals on generalized derivations-I. arXiv."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/4\/247\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:59:41Z","timestamp":1760029181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/4\/247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["axioms14040247"],"URL":"https:\/\/doi.org\/10.3390\/axioms14040247","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,25]]}}}