{"id":"https://openalex.org/W7213512941","doi":"https://doi.org/10.13140/rg.2.2.26878.34882","title":"THE FINITE BASIS PROBLEM FOR ADDITIVELY IDEMPOTENT SEMIRINGS OF ORDER FOUR, IV","display_name":"THE FINITE BASIS PROBLEM FOR ADDITIVELY IDEMPOTENT SEMIRINGS OF ORDER FOUR, IV","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213512941","doi":"https://doi.org/10.13140/rg.2.2.26878.34882"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32152","pdf_url":"https://arxiv.org/pdf/2609.32152","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.32152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134253680","display_name":"Miaomiao Ren","orcid":"https://orcid.org/0000-0003-1337-0919","observed_orcids":["https://orcid.org/0000-0003-1337-0919"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miaomiao Ren","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122939508","display_name":"Mengya Yue","orcid":"https://orcid.org/0009-0002-3939-947X","observed_orcids":["https://orcid.org/0009-0002-3939-947X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mengya Yue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152035195","display_name":"Mengyu Yuan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mengyu Yuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012045037","display_name":"Simin Lyu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simin Lyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152017141","display_name":"Chenyu Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chenyu Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101350497","display_name":"Ting Yu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ting Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.7378000020980835,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.7378000020980835,"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/T11567","display_name":"semigroups and automata theory","score":0.23800000548362732,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.00559999980032444,"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/finite-basis-problem","display_name":"finite basis problem","score":0.9789999723434448},{"id":"https://openalex.org/keywords/additively-idempotent-semirings","display_name":"additively idempotent semirings","score":0.9409999847412109},{"id":"https://openalex.org/keywords/chains","display_name":"chains","score":0.7850000262260437}],"concepts":[{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.6419000029563904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6049000024795532},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38960000872612},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31459999084472656},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2833999991416931},{"id":"https://openalex.org/C33375987","wikidata":"https://www.wikidata.org/wiki/Q3751720","display_name":"Idempotent matrix","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.26930001378059387}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.32152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32152","pdf_url":"https://arxiv.org/pdf/2609.32152","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.32152","doi":"https://doi.org/10.48550/arxiv.2609.32152","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32152","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.13140/rg.2.2.26878.34882","doi":"https://doi.org/10.13140/rg.2.2.26878.34882","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.26878.34882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32152","pdf_url":"https://arxiv.org/pdf/2609.32152","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3090029520","display_name":null,"funder_award_id":"12571020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7299353239","display_name":null,"funder_award_id":"12371024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213512941.pdf","grobid_xml":"https://content.openalex.org/works/W7213512941.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4362728206","https://openalex.org/W4389364063","https://openalex.org/W4407091202","https://openalex.org/W7161561314","https://openalex.org/W7166308815"],"related_works":["https://openalex.org/W6891967761","https://openalex.org/W4415401949","https://openalex.org/W4409261003","https://openalex.org/W7215100707","https://openalex.org/W7133340010","https://openalex.org/W7161561314","https://openalex.org/W7213595988","https://openalex.org/W4415252536","https://openalex.org/W7128555724","https://openalex.org/W7222532415"],"abstract_inverted_index":{"This":[0,78],"paper":[1],"is":[2],"the":[3,10,33,80,85],"fourth":[4],"in":[5],"a":[6],"series":[7],"devoted":[8],"to":[9,27,46,84],"finite":[11,86],"basis":[12,87],"problem":[13],"for":[14],"$4$-element":[15,91],"additively":[16,92],"idempotent":[17,93],"semirings.":[18],"These":[19],"algebras":[20],"are":[21,43,49,75],"divided":[22],"into":[23],"five":[24],"types":[25],"according":[26],"their":[28],"additive":[29,41,97],"reducts;":[30],"we":[31],"study":[32],"largest":[34],"of":[35,68,89],"these":[36],"types,":[37],"namely":[38,70],"those":[39],"whose":[40],"reducts":[42],"chains.":[44],"Up":[45],"isomorphism,":[47],"there":[48],"$386$":[50],"such":[51],"algebras,":[52],"denoted":[53],"by":[54],"$S_{(4,":[55],"k)}$,":[56],"$481":[57],"\\leq":[58,60],"k":[59],"866$.":[61],"We":[62],"show":[63],"that":[64],"all":[65,90],"but":[66],"three":[67],"them,":[69],"$S_{(4,545)}$,":[71],"$S_{(4,634)}$,":[72],"and":[73],"$S_{(4,710)}$,":[74],"finitely":[76],"based.":[77],"completes":[79],"classification,":[81],"with":[82,95],"respect":[83],"property,":[88],"semirings":[94],"chain":[96],"reducts.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-18T00:00:00"}