{"id":"https://openalex.org/W4298003892","doi":"https://doi.org/10.3390/sym14102015","title":"\ud835\udca9-Structures Applied to Commutative Ideals of BCI-Algebras","display_name":"\ud835\udca9-Structures Applied to Commutative Ideals of BCI-Algebras","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W4298003892","doi":"https://doi.org/10.3390/sym14102015"},"language":"en","primary_location":{"id":"doi:10.3390/sym14102015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102015","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2015/pdf?version=1665364026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/10/2015/pdf?version=1665364026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035644463","display_name":"G. Muhiuddin","orcid":"https://orcid.org/0000-0002-5596-5841"},"institutions":[{"id":"https://openalex.org/I72264486","display_name":"University of Tabuk","ror":"https://ror.org/04yej8x59","country_code":"SA","type":"education","lineage":["https://openalex.org/I72264486"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ghulam Muhiuddin","raw_affiliation_strings":["Algebra, Discrete Mathematics and Number Theory Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Algebra, Discrete Mathematics and Number Theory Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia","institution_ids":["https://openalex.org/I72264486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047616136","display_name":"Mohamed E. A. Elnair","orcid":null},"institutions":[{"id":"https://openalex.org/I72264486","display_name":"University of Tabuk","ror":"https://ror.org/04yej8x59","country_code":"SA","type":"education","lineage":["https://openalex.org/I72264486"]},{"id":"https://openalex.org/I78157869","display_name":"University of Gezira","ror":"https://ror.org/001mf9v16","country_code":"SD","type":"education","lineage":["https://openalex.org/I78157869"]}],"countries":["SA","SD"],"is_corresponding":false,"raw_author_name":"Mohamed E. Elnair","raw_affiliation_strings":["Algebra, Discrete Mathematics and Number Theory Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia","Department of Mathematics and Physics, Gezira University, P.O. Box 20, Wad Medani 2667, Sudan"],"affiliations":[{"raw_affiliation_string":"Algebra, Discrete Mathematics and Number Theory Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia","institution_ids":["https://openalex.org/I72264486"]},{"raw_affiliation_string":"Department of Mathematics and Physics, Gezira University, P.O. Box 20, Wad Medani 2667, Sudan","institution_ids":["https://openalex.org/I78157869"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020053606","display_name":"Deena Al-Kadi","orcid":"https://orcid.org/0000-0001-7899-1578"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Deena Al-Kadi","raw_affiliation_strings":["Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035644463"],"corresponding_institution_ids":["https://openalex.org/I72264486"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3273,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61926991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"10","first_page":"2015","last_page":"2015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9973000288009644,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9829999804496765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.7617825865745544},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.7495995163917542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6944435238838196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5436834692955017},{"id":"https://openalex.org/keywords/ideal-theory","display_name":"Ideal theory","score":0.5231512784957886},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45099306106567383},{"id":"https://openalex.org/keywords/primary-ideal","display_name":"Primary ideal","score":0.43866872787475586},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4355491101741791},{"id":"https://openalex.org/keywords/fractional-ideal","display_name":"Fractional ideal","score":0.4283081293106079},{"id":"https://openalex.org/keywords/maximal-ideal","display_name":"Maximal ideal","score":0.42760002613067627},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4158868193626404},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.2737317383289337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13502320647239685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07623150944709778},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.0603976845741272}],"concepts":[{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.7617825865745544},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.7495995163917542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6944435238838196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5436834692955017},{"id":"https://openalex.org/C23573486","wikidata":"https://www.wikidata.org/wiki/Q1952929","display_name":"Ideal theory","level":4,"score":0.5231512784957886},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45099306106567383},{"id":"https://openalex.org/C170320730","wikidata":"https://www.wikidata.org/wiki/Q1142699","display_name":"Primary ideal","level":5,"score":0.43866872787475586},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4355491101741791},{"id":"https://openalex.org/C182817911","wikidata":"https://www.wikidata.org/wiki/Q1497184","display_name":"Fractional ideal","level":3,"score":0.4283081293106079},{"id":"https://openalex.org/C118211362","wikidata":"https://www.wikidata.org/wiki/Q1203540","display_name":"Maximal ideal","level":3,"score":0.42760002613067627},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4158868193626404},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.2737317383289337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13502320647239685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07623150944709778},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0603976845741272},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C156923205","wikidata":"https://www.wikidata.org/wiki/Q2905043","display_name":"Principal ideal ring","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14102015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102015","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2015/pdf?version=1665364026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1b82638f528649d88ebeeb86905b3fc6","is_oa":true,"landing_page_url":"https://doaj.org/article/1b82638f528649d88ebeeb86905b3fc6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 10, p 2015 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/2015/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14102015","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14102015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102015","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2015/pdf?version=1665364026","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4298003892.pdf","grobid_xml":"https://content.openalex.org/works/W4298003892.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W270672333","https://openalex.org/W284997383","https://openalex.org/W1558143288","https://openalex.org/W1981523482","https://openalex.org/W2007132618","https://openalex.org/W2011765234","https://openalex.org/W2029515491","https://openalex.org/W2083301283","https://openalex.org/W2110963958","https://openalex.org/W2521399310","https://openalex.org/W2766342865","https://openalex.org/W2782766576","https://openalex.org/W2885877913","https://openalex.org/W2902468645","https://openalex.org/W2941711940","https://openalex.org/W2967666729","https://openalex.org/W2997185571","https://openalex.org/W3014152749","https://openalex.org/W3095637875","https://openalex.org/W3124241913","https://openalex.org/W3163657479","https://openalex.org/W4211007335","https://openalex.org/W4393004378","https://openalex.org/W4393005274","https://openalex.org/W6676995870","https://openalex.org/W6772674457","https://openalex.org/W6775557102","https://openalex.org/W6796148443","https://openalex.org/W6892440643"],"related_works":["https://openalex.org/W2599483862","https://openalex.org/W2077106549","https://openalex.org/W2031479614","https://openalex.org/W307015568","https://openalex.org/W2322706357","https://openalex.org/W2002128832","https://openalex.org/W2766342865","https://openalex.org/W3217209015","https://openalex.org/W2011501578","https://openalex.org/W233203565"],"abstract_inverted_index":{"The":[0],"study":[1],"of":[2,6,16,60,71,76,87,102],"symmetry":[3],"is":[4,62,91,118,122,132],"one":[5],"the":[7,55,58,65,68,85],"most":[8],"important":[9],"and":[10,78,93],"beautiful":[11],"themes":[12],"uniting":[13],"various":[14],"areas":[15],"contemporary":[17],"arithmetic.":[18],"Algebraic":[19],"structures":[20,23],"are":[21,82,96,105],"useful":[22,100],"in":[24,80,125],"pure":[25],"mathematics":[26],"for":[27,40,109],"learning":[28],"a":[29,37,45,88,110,115,126,133],"geometrical":[30],"object\u2019s":[31],"symmetries.":[32],"In":[33,54,98],"order":[34],"to":[35,64,113],"provide":[36],"mathematical":[38],"tool":[39],"dealing":[41],"with":[42,52],"negative":[43],"information,":[44],"negative-valued":[46],"function":[47],"came":[48],"into":[49],"existence":[50],"along":[51],"N-structures.":[53],"present":[56],"analysis,":[57],"notion":[59,86],"N-structures":[61],"applied":[63],"ideals,":[66],"especially":[67],"commutative":[69,89,103,116,127,134],"ideals":[70],"BCI-algebras.":[72],"Firstly,":[73],"several":[74],"properties":[75,95],"N-subalgebras":[77],"N-ideals":[79,104],"BCI-algebras":[81],"investigated.":[83,97],"Furthermore,":[84],"N-ideal":[90,112,117,131],"defined,":[92],"related":[94],"addition,":[99],"characterizations":[101],"established.":[106],"A":[107],"condition":[108],"closed":[111,130],"be":[114],"provided.":[119],"Finally,":[120],"it":[121],"proved":[123],"that":[124],"BCI-algebra,":[128],"every":[129],"N-ideal.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}