{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T20:12:04Z","timestamp":1768680724993,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Technological Development and Innovation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Omega rings (\u03a9-rings) (and other related structures) are lattice-valued structures (with \u03a9 being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, \u03a9-ideals are introduced, and natural connections with \u03a9-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over \u03a9-fields is developed.<\/jats:p>","DOI":"10.3390\/axioms12080757","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T09:32:35Z","timestamp":1690882355000},"page":"757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3159-3721","authenticated-orcid":false,"given":"Jorge","family":"Jimenez","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8643-2733","authenticated-orcid":false,"given":"Mar\u00eda Luisa","family":"Serrano","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Branimir","family":"\u0160e\u0161elja","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5716-604X","authenticated-orcid":false,"given":"Andreja","family":"Tepav\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia"},{"name":"Mathematical Institute SANU, 11000 Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.fss.2022.04.012","article-title":"Omega-rings","volume":"455","author":"Jimenez","year":"2023","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/0022-247X(81)90164-5","article-title":"Fuzzy groups and level subgroups","volume":"84","author":"Das","year":"1981","journal-title":"J. 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