{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:34:33Z","timestamp":1753882473950,"version":"3.41.2"},"reference-count":6,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T00:00:00Z","timestamp":1726617600000},"content-version":"vor","delay-in-days":261,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>This paper offers an in\u2010depth investigation into pure ideals within the Hurwitz series ring. Specifically, by focusing on the Hurwitz series ring, denoted as <jats:italic>H<\/jats:italic><jats:italic>R<\/jats:italic> over a ring <jats:italic>R<\/jats:italic>, we present a comprehensive characterization of differential ideals. In this paper, we prove that these differential ideals can be expressed in the form <jats:italic>H<\/jats:italic><jats:italic>I<\/jats:italic>, where <jats:italic>I<\/jats:italic> represents an ideal in the underlying ring <jats:italic>R<\/jats:italic>. Through this analysis, a comprehensive understanding of the structure and properties of pure ideals within the Hurwitz series ring is achieved.<\/jats:p>","DOI":"10.1155\/2024\/9412822","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T13:19:13Z","timestamp":1726665553000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Characterization of Differential and Pure Ideals in the Hurwitz Series Ring: Structural Insights and Formulations"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1145-0256","authenticated-orcid":false,"given":"Omar","family":"Alomari","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3756-8110","authenticated-orcid":false,"given":"Manal","family":"Al-Labadi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2024,9,18]]},"reference":[{"key":"e_1_2_5_1_2","first-page":"251","article-title":"Ideal structure of hurwitz series ring","volume":"1","author":"Benhissi A.","year":"2007","journal-title":"Contributions to Algebra and Geometry"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00927879708825957"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.4064\/bc94-0-13"},{"key":"e_1_2_5_4_2","article-title":"On some properties of polynomial rings","volume":"14","author":"Al-Ezeh H.","year":"1987","journal-title":"International Journal Mathematics and Science"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01277063"},{"key":"e_1_2_5_6_2","first-page":"289","article-title":"Projectivity of pure ideals","volume":"68","author":"DeMarco G.","year":"1983","journal-title":"Rendiconti del Seminario Matematico della Universit\u00e0 di Padova"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2024\/9412822","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T13:19:16Z","timestamp":1726665556000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2024\/9412822"}},"subtitle":[],"editor":[{"given":"Abdul Rauf","family":"Khan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["10.1155\/2024\/9412822"],"URL":"https:\/\/doi.org\/10.1155\/2024\/9412822","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2024,1]]},"assertion":[{"value":"2023-12-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-09-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-09-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"9412822"}}