{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:59:18Z","timestamp":1760147958084,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T00:00:00Z","timestamp":1679011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this study is to provide a generalization of prime vague \u0393-ideals in \u0393-rings by introducing non-symmetric 2-absorbing vague weakly complete \u0393-ideals of commutative \u0393-rings. A novel algebraic structure of a primary vague \u0393-ideal of a commutative \u0393-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague \u0393-ideals of \u0393-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete \u0393-ideals and 2-absorbing \u0393-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete \u0393-ideal of a \u0393-ring and 2-absorbing K-vague \u0393-ideal of a \u0393-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient \u0393-ring of R induced by a 2-absorbing vague weakly complete \u0393-ideal of a 2-absorbing \u0393-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing \u0393-ideal.<\/jats:p>","DOI":"10.3390\/sym15030740","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T04:10:48Z","timestamp":1679026248000},"page":"740","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["2-Absorbing Vague Weakly Complete \u0393-Ideals in \u0393-Rings"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3084-7694","authenticated-orcid":false,"given":"Serkan","family":"Onar","sequence":"first","affiliation":[{"name":"Department of Mathematical Engineering, Yildiz Technical University, Davutpa\u015fa-Istanbul 34349, T\u00fcrkiye"}]},{"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, 1000 Tiran\u00eb, Albania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-1800","authenticated-orcid":false,"given":"Sina","family":"Etemad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Computer Science & Mathematics, Lebanese American University, Beirut 5053, Lebanon"},{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, T\u00fcrkiye"},{"name":"Mathematics Research Center, Department of Mathematics, Near East University, North Cyprus, Mersin 10, Nicosia 99138, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV\/EHU), 48940 Leioa, Bizkaia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3463-2607","authenticated-orcid":false,"given":"Shahram","family":"Rezapour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"},{"name":"Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1017\/S0004972700039344","article-title":"On 2-absorbing ideals of commutative rings","volume":"75","author":"Badawi","year":"2007","journal-title":"Bull. 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