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We demonstrate a few intermediate findings about the localization of a noetherian domain at its fuzzy fractional ideals. Introducing the new concepts and provide some examples via discrete valuation ring illustrates that a discrete valuation ring is the localization of a noetherian domain at its fuzzy fractional ideals.<\/jats:p>","DOI":"10.1142\/s1793005726500511","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T22:40:51Z","timestamp":1741732851000},"page":"1025-1038","source":"Crossref","is-referenced-by-count":0,"title":["An Innovative Unique Factorization Approach of Fuzzy Fractional Ideals in Dedekind Domains"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4740-4022","authenticated-orcid":false,"given":"Tasaduk Rashid","family":"Mir","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3283-1410","authenticated-orcid":false,"given":"M.","family":"Yahya Abbasi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6425-2619","authenticated-orcid":false,"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, Polytechnic University of Tirana, Tiran\u00eb, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5746-0619","authenticated-orcid":false,"given":"Shahnawaz","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi 110025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"S1793005726500511BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"S1793005726500511BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00414-4"},{"key":"S1793005726500511BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00032-X"},{"key":"S1793005726500511BIB004","doi-asserted-by":"publisher","DOI":"10.1080\/03081079008935107"},{"key":"S1793005726500511BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90199-5"},{"key":"S1793005726500511BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(82)90003-3"},{"key":"S1793005726500511BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(83)80067-0"},{"key":"S1793005726500511BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(90)90066-F"},{"key":"S1793005726500511BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(91)90038-V"},{"key":"S1793005726500511BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(91)90011-I"},{"key":"S1793005726500511BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90155-2"},{"key":"S1793005726500511BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(88)90009-1"},{"key":"S1793005726500511BIB013","doi-asserted-by":"publisher","DOI":"10.1216\/rmjm\/1181072497"},{"key":"S1793005726500511BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00321-5"},{"key":"S1793005726500511BIB015","volume-title":"Advances in Fuzzy Theory and Technology","volume":"1","author":"Mordeson J. 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