{"id":"https://openalex.org/W4385446642","doi":"https://doi.org/10.3390/axioms12080757","title":"Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields","display_name":"Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4385446642","doi":"https://doi.org/10.3390/axioms12080757"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12080757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080757","pdf_url":"https://www.mdpi.com/2075-1680/12/8/757/pdf?version=1690873467","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/8/757/pdf?version=1690873467","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040862315","display_name":"Jorge Jim\u00e9nez","orcid":"https://orcid.org/0000-0002-3159-3721"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jorge Jimenez","raw_affiliation_strings":["Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain"],"raw_orcid":"https://orcid.org/0000-0002-3159-3721","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086946679","display_name":"Mar\u00eda Luisa Serrano","orcid":"https://orcid.org/0000-0001-8643-2733"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda Luisa Serrano","raw_affiliation_strings":["Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8643-2733","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033430549","display_name":"Branimir \u0160e\u0161elja","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Branimir \u0160e\u0161elja","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047239495","display_name":"Andreja Tepav\u010devi\u0107","orcid":"https://orcid.org/0000-0002-5716-604X"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]},{"id":"https://openalex.org/I4210113556","display_name":"Institut za savremenu istoriju","ror":"https://ror.org/01y6sx232","country_code":"RS","type":"facility","lineage":["https://openalex.org/I4210113556"]},{"id":"https://openalex.org/I4390039372","display_name":"Mathematical Institute of the Serbian Academy of Sciences and Arts","ror":"https://ror.org/02jxk1021","country_code":null,"type":"education","lineage":["https://openalex.org/I1338511612","https://openalex.org/I4390039372"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Andreja Tepav\u010devi\u0107","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia","Mathematical Institute SANU, 11000 Beograd, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-5716-604X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]},{"raw_affiliation_string":"Mathematical Institute SANU, 11000 Beograd, Serbia","institution_ids":["https://openalex.org/I4210113556","https://openalex.org/I4390039372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047239495"],"corresponding_institution_ids":["https://openalex.org/I170726198","https://openalex.org/I4210113556","https://openalex.org/I4390039372"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.3853,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63408548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"12","issue":"8","first_page":"757","last_page":"757"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.8454940915107727},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.7422029972076416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6021424531936646},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5846486687660217},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5634755492210388},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.5547971725463867},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2038957178592682},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13365784287452698}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.8454940915107727},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7422029972076416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6021424531936646},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5846486687660217},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5634755492210388},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.5547971725463867},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2038957178592682},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13365784287452698},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12080757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080757","pdf_url":"https://www.mdpi.com/2075-1680/12/8/757/pdf?version=1690873467","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:130d9f96d0f7481b9912c30b04818f09","is_oa":true,"landing_page_url":"https://doaj.org/article/130d9f96d0f7481b9912c30b04818f09","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 8, p 757 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/8/757/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12080757","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12080757","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080757","pdf_url":"https://www.mdpi.com/2075-1680/12/8/757/pdf?version=1690873467","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385446642.pdf","grobid_xml":"https://content.openalex.org/works/W4385446642.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W182232724","https://openalex.org/W648107711","https://openalex.org/W1557351111","https://openalex.org/W1985910473","https://openalex.org/W2000594950","https://openalex.org/W2001470915","https://openalex.org/W2012098656","https://openalex.org/W2021517236","https://openalex.org/W2027184909","https://openalex.org/W2030259157","https://openalex.org/W2054416947","https://openalex.org/W2055487540","https://openalex.org/W2096768134","https://openalex.org/W2106869653","https://openalex.org/W2128084377","https://openalex.org/W2149467658","https://openalex.org/W2157258865","https://openalex.org/W2190325362","https://openalex.org/W2506954980","https://openalex.org/W2585574173","https://openalex.org/W2778173235","https://openalex.org/W2913061926","https://openalex.org/W2940753058","https://openalex.org/W2969977995","https://openalex.org/W3015736449","https://openalex.org/W4210778630","https://openalex.org/W4213103183","https://openalex.org/W4224437633","https://openalex.org/W4236918858","https://openalex.org/W4293176479","https://openalex.org/W6746931342","https://openalex.org/W7038940180"],"related_works":["https://openalex.org/W2778946875","https://openalex.org/W2023974151","https://openalex.org/W2163207601","https://openalex.org/W4301322097","https://openalex.org/W3049507786","https://openalex.org/W2103827354","https://openalex.org/W2590546754","https://openalex.org/W4293173044","https://openalex.org/W2472631239","https://openalex.org/W2964315014"],"abstract_inverted_index":{"Omega":[0],"rings":[1],"(\u03a9-rings)":[2],"(and":[3],"other":[4],"related":[5],"structures)":[6],"are":[7,35,44],"lattice-valued":[8,25],"structures":[9],"(with":[10],"\u03a9":[11],"being":[12],"the":[13,21,28],"codomain":[14],"lattice)":[15],"defined":[16],"on":[17],"crisp":[18],"algebras":[19],"of":[20,51,54,56],"same":[22],"type,":[23],"with":[24,40],"equality":[26],"replacing":[27],"classical":[29],"one.":[30],"In":[31],"this":[32],"paper,":[33],"\u03a9-ideals":[34],"introduced,":[36],"and":[37,42],"natural":[38],"connections":[39],"\u03a9-congruences":[41],"homomorphisms":[43],"established.":[45],"As":[46],"an":[47],"application,":[48],"a":[49],"framework":[50],"approximate":[52],"solutions":[53],"systems":[55],"linear":[57],"equations":[58],"over":[59],"\u03a9-fields":[60],"is":[61],"developed.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}