{"id":"https://openalex.org/W4307944524","doi":"https://doi.org/10.3390/sym14112265","title":"Some Aspects of Hyperatom Elements in Ordered Semihyperrings","display_name":"Some Aspects of Hyperatom Elements in Ordered Semihyperrings","publication_year":2022,"publication_date":"2022-10-28","ids":{"openalex":"https://openalex.org/W4307944524","doi":"https://doi.org/10.3390/sym14112265"},"language":"en","primary_location":{"id":"doi:10.3390/sym14112265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112265","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2265/pdf?version=1666948471","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/2073-8994/14/11/2265/pdf?version=1666948471","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081956455","display_name":"Zheng Kou","orcid":"https://orcid.org/0000-0003-4758-2872"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Kou","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006042809","display_name":"Mehdi Gheisari","orcid":"https://orcid.org/0000-0002-5643-0021"},"institutions":[{"id":"https://openalex.org/I85461943","display_name":"Saveetha University","ror":"https://ror.org/0034me914","country_code":"IN","type":"education","lineage":["https://openalex.org/I85461943"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Mehdi Gheisari","raw_affiliation_strings":["Department of Cognitive Computing, Institute of Computer Science and Engineering, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Cognitive Computing, Institute of Computer Science and Engineering, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India","institution_ids":["https://openalex.org/I85461943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056996250","display_name":"Kostaq Hila","orcid":"https://orcid.org/0000-0001-6425-2619"},"institutions":[{"id":"https://openalex.org/I193184871","display_name":"Polytechnic University of Tirana","ror":"https://ror.org/05aec4025","country_code":"AL","type":"education","lineage":["https://openalex.org/I193184871"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Kostaq Hila","raw_affiliation_strings":["Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana 1001, Albania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana 1001, Albania","institution_ids":["https://openalex.org/I193184871"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016481396","display_name":"Nategh Abbasizadeh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108141","display_name":"Ministry of Education","ror":"https://ror.org/01hw7wf62","country_code":"IR","type":"government","lineage":["https://openalex.org/I4210108141"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Nategh Abbasizadeh","raw_affiliation_strings":["Department of Education, Ministry of Education Iran, Shiraz 73, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Education, Ministry of Education Iran, Shiraz 73, Iran","institution_ids":["https://openalex.org/I4210108141"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006042809"],"corresponding_institution_ids":["https://openalex.org/I85461943"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2996,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60232657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"11","first_page":"2265","last_page":"2265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994000196456909,"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":0.9994000196456909,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9570000171661377,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monomorphism","display_name":"Monomorphism","score":0.7598106861114502},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7404088973999023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6436312198638916},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6251978874206543},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.44795289635658264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39805519580841064},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.2736847400665283},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09132641553878784},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.08314833045005798}],"concepts":[{"id":"https://openalex.org/C100036529","wikidata":"https://www.wikidata.org/wiki/Q1945067","display_name":"Monomorphism","level":3,"score":0.7598106861114502},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7404088973999023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6436312198638916},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6251978874206543},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.44795289635658264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39805519580841064},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.2736847400665283},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09132641553878784},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.08314833045005798},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14112265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112265","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2265/pdf?version=1666948471","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:578fc964066d40a0a4450f18e734f802","is_oa":true,"landing_page_url":"https://doaj.org/article/578fc964066d40a0a4450f18e734f802","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":"Symmetry, Vol 14, Iss 11, p 2265 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/11/2265/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14112265","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; Volume 14; Issue 11; Pages: 2265","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14112265","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112265","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2265/pdf?version=1666948471","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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307944524.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W790387146","https://openalex.org/W1484040084","https://openalex.org/W2056838618","https://openalex.org/W2162097202","https://openalex.org/W2184403059","https://openalex.org/W2231439918","https://openalex.org/W2340348564","https://openalex.org/W2409879651","https://openalex.org/W2762142437","https://openalex.org/W2789703518","https://openalex.org/W2790284152","https://openalex.org/W2890791798","https://openalex.org/W2912215743","https://openalex.org/W2963646956","https://openalex.org/W3097828265","https://openalex.org/W3100749828","https://openalex.org/W3162464328","https://openalex.org/W3163873911","https://openalex.org/W3207869441","https://openalex.org/W3209571057","https://openalex.org/W4200284276","https://openalex.org/W6622735147","https://openalex.org/W6689428732","https://openalex.org/W6703977120","https://openalex.org/W6714441814","https://openalex.org/W6744744380","https://openalex.org/W6754352167","https://openalex.org/W6766777117"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2963909210","https://openalex.org/W1592193675","https://openalex.org/W2092684517","https://openalex.org/W2953362199","https://openalex.org/W2061114238","https://openalex.org/W2089269623","https://openalex.org/W3114459035","https://openalex.org/W2357235461","https://openalex.org/W230476045"],"abstract_inverted_index":{"In":[0],"this":[1,38],"paper,":[2],"first,":[3],"we":[4,75,88],"state":[5],"an":[6,10,80,94],"operator":[7],"LR":[8],"on":[9],"ordered":[11,30,60,81],"semihyperring":[12,61,82],"R.":[13,51],"We":[14,52],"show":[15,89],"that":[16,54,72,90],"if":[17,55,91],"\u03c6:R\u27f6T":[18,92],"is":[19,57,93,97,104],"a":[20,58],"monomorphism":[21],"and":[22,34,62,83,102],"K\u2286R,":[23],"then":[24,64,109],"LT(\u03c6(K))=\u03c6(LR(K)).":[25],"Afterward,":[26],"hyperatom":[27],"elements":[28],"in":[29,37],"semihyperrings":[31],"are":[32,40],"defined":[33],"some":[35,85],"results":[36],"respect":[39],"investigated.":[41],"Denote":[42],"by":[43],"A(R)":[44],"the":[45,77,98,105],"set":[46],"of":[47,50,79,100,107],"all":[48],"hyperatoms":[49],"prove":[53],"R":[56,101],"finite":[59],"|R|\u22652,":[63],"for":[65],"any":[66],"q\u2208R\\{0},":[67],"there":[68],"exists":[69],"hq\u2208A*(R)=A(R)\\{0}":[70],"such":[71],"hq\u2264q.":[73],"Finally,":[74],"study":[76],"LR-graph":[78,99],"give":[84],"examples.":[86],"Furthermore,":[87],"isomorphism,":[95],"G":[96],"G\u2032":[103],"LT-graph":[106],"T,":[108],"G\u2245G\u2032.":[110]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
