{"id":"https://openalex.org/W4391219230","doi":"https://doi.org/10.3390/axioms13020081","title":"A Hyperstructural Approach to Semisimplicity","display_name":"A Hyperstructural Approach to Semisimplicity","publication_year":2024,"publication_date":"2024-01-25","ids":{"openalex":"https://openalex.org/W4391219230","doi":"https://doi.org/10.3390/axioms13020081"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13020081","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020081","pdf_url":"https://www.mdpi.com/2075-1680/13/2/81/pdf?version=1706191725","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/2075-1680/13/2/81/pdf?version=1706191725","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082670019","display_name":"Erg\u00fcl T\u00fcrkmen","orcid":"https://orcid.org/0000-0002-7082-1176"},"institutions":[{"id":"https://openalex.org/I70387731","display_name":"Amasya \u00dcniversitesi","ror":"https://ror.org/00sbx0y13","country_code":"TR","type":"education","lineage":["https://openalex.org/I70387731"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erg\u00fcl T\u00fcrkmen","raw_affiliation_strings":["Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey","institution_ids":["https://openalex.org/I70387731"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057281155","display_name":"Burcu Ni\u015fanc\u0131 T\u00fcrkmen","orcid":null},"institutions":[{"id":"https://openalex.org/I70387731","display_name":"Amasya \u00dcniversitesi","ror":"https://ror.org/00sbx0y13","country_code":"TR","type":"education","lineage":["https://openalex.org/I70387731"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Burcu N\u0130\u015fanc\u0131 T\u00fcrkmen","raw_affiliation_strings":["Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-7900-0529","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Ipekkoy, Turkey","institution_ids":["https://openalex.org/I70387731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061256797","display_name":"Hashem Bordbar","orcid":"https://orcid.org/0000-0003-3871-217X"},"institutions":[{"id":"https://openalex.org/I192455894","display_name":"University of Nova Gorica","ror":"https://ror.org/00mw0tw28","country_code":"SI","type":"education","lineage":["https://openalex.org/I192455894"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Hashem Bordbar","raw_affiliation_strings":["Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"],"raw_orcid":"https://orcid.org/0000-0003-3871-217X","affiliations":[{"raw_affiliation_string":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia","institution_ids":["https://openalex.org/I192455894"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061256797"],"corresponding_institution_ids":["https://openalex.org/I192455894"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.6322,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.91295356,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"13","issue":"2","first_page":"81","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998000264167786,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9966999888420105,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.992900013923645,"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/computer-science","display_name":"Computer science","score":0.3664896786212921}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3664896786212921}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13020081","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020081","pdf_url":"https://www.mdpi.com/2075-1680/13/2/81/pdf?version=1706191725","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:repozitorij.ung.si:IzpisGradiva.php?id=8838","is_oa":true,"landing_page_url":"https://repozitorij.ung.si/Dokument.php?id=28233&dn=","pdf_url":"https://repozitorij.ung.si/Dokument.php?id=28231&dn=","source":{"id":"https://openalex.org/S7407055115","display_name":"RUNG","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 2075-1680","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:2d0044ec012b4438b46b8c3db6337a95","is_oa":true,"landing_page_url":"https://doaj.org/article/2d0044ec012b4438b46b8c3db6337a95","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 13, Iss 2, p 81 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13020081","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020081","pdf_url":"https://www.mdpi.com/2075-1680/13/2/81/pdf?version=1706191725","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391219230.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1497483297","https://openalex.org/W1963795372","https://openalex.org/W2007388994","https://openalex.org/W2057715074","https://openalex.org/W2061569997","https://openalex.org/W2151290870","https://openalex.org/W2164139224","https://openalex.org/W2618542559","https://openalex.org/W2791532510","https://openalex.org/W2800861293","https://openalex.org/W2898844467","https://openalex.org/W2906026575","https://openalex.org/W2911066197","https://openalex.org/W2914173484","https://openalex.org/W2929195203","https://openalex.org/W2964108585","https://openalex.org/W2964201195","https://openalex.org/W2978049082","https://openalex.org/W3035247574","https://openalex.org/W3048826877","https://openalex.org/W3106981640","https://openalex.org/W3126595280","https://openalex.org/W3157245431","https://openalex.org/W3159215254","https://openalex.org/W4221033542","https://openalex.org/W6641166865","https://openalex.org/W6758907186","https://openalex.org/W6786655854","https://openalex.org/W6809764908","https://openalex.org/W6996682907"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W1596801655","https://openalex.org/W2359140296"],"abstract_inverted_index":{"In":[0,69],"this":[1],"paper,":[2],"we":[3,71],"provide":[4],"the":[5,28,54],"basic":[6],"properties":[7],"of":[8,30,34,56,75,79,81],"(semi)simple":[9],"hypermodules.":[10],"We":[11,36,50],"show":[12,52],"that":[13,38,53],"if":[14],"a":[15,23,46,73,82],"hypermodule":[16,41],"M":[17],"is":[18,22,27,42,59],"simple,":[19],"then":[20],"(End(M),\u00b7)":[21],"group,":[24],"where":[25],"End(M)":[26],"set":[29],"all":[31],"normal":[32,43],"endomorphisms":[33],"M.":[35],"prove":[37],"every":[39],"simple":[40],"projective":[44],"with":[45],"zero":[47],"singular":[48],"subhypermodule.":[49],"also":[51],"class":[55],"semisimple":[57],"hypermodules":[58],"closed":[60],"under":[61],"internal":[62,76],"direct":[63,77],"sums,":[64],"factor":[65],"hypermodules,":[66],"and":[67],"subhypermodules.":[68],"particular,":[70],"give":[72],"characterization":[74],"sums":[78],"subhypermodules":[80],"hypermodule.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}