{"id":"https://openalex.org/W7222995324","doi":"https://doi.org/10.48550/arxiv.2610.24120","title":"Derivations of the idealization of the incidence module over the finitary incidence algebra","display_name":"Derivations of the idealization of the incidence module over the finitary incidence algebra","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222995324","doi":"https://doi.org/10.48550/arxiv.2610.24120"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.24120","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24120","pdf_url":"https://arxiv.org/pdf/2610.24120","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/2610.24120","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159158765","display_name":"\u00c9rica Zancanella Fornaroli","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fornaroli, \u00c9rica Zancanella","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidade Estadual de Maring\u00e1 , Avenida Colombo , 5790 , Maring\u00e1 , PR , 87020-900 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidade Estadual de Maring\u00e1 , Avenida Colombo , 5790 , Maring\u00e1 , PR , 87020-900 , Brazil","institution_ids":["https://openalex.org/I123443094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006033820","display_name":"Roger Emanuel Moraes Pezzott","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Pezzott, Roger Emanuel Moraes","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidade Estadual de Maring\u00e1 , Avenida Colombo , 5790 , Maring\u00e1 , PR , 87020-900 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidade Estadual de Maring\u00e1 , Avenida Colombo , 5790 , Maring\u00e1 , PR , 87020-900 , Brazil","institution_ids":["https://openalex.org/I123443094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I123443094"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11673","display_name":"Advanced Topics in Algebra","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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.04179999977350235,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/idealization","display_name":"idealization","score":0.699999988079071},{"id":"https://openalex.org/keywords/derivations","display_name":"derivations","score":0.8169999718666077},{"id":"https://openalex.org/keywords/lie-algebras-of-derivations","display_name":"Lie algebras of derivations","score":0.9769999980926514},{"id":"https://openalex.org/keywords/partial-orders","display_name":"partially ordered sets","score":0.9739999771118164},{"id":"https://openalex.org/keywords/commutative-rings","display_name":"commutative rings","score":0.8140000104904175},{"id":"https://openalex.org/keywords/bimodules","display_name":"bimodules","score":0.8999999761581421}],"concepts":[{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.8733000159263611},{"id":"https://openalex.org/C2780986378","wikidata":"https://www.wikidata.org/wiki/Q776634","display_name":"Idealization","level":2,"score":0.8033999800682068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7634999752044678},{"id":"https://openalex.org/C115179944","wikidata":"https://www.wikidata.org/wiki/Q371133","display_name":"Incidence algebra","level":5,"score":0.7421000003814697},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.6491000056266785},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5738999843597412},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5473999977111816},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.5249999761581421},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5123999714851379},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.46889999508857727},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.460999995470047},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.40720000863075256},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C2781106287","wikidata":"https://www.wikidata.org/wiki/Q806066","display_name":"Banach algebra","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.3343000113964081},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C125225535","wikidata":"https://www.wikidata.org/wiki/Q7049224","display_name":"Noncommutative ring","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C51292594","wikidata":"https://www.wikidata.org/wiki/Q744960","display_name":"Associative algebra","level":5,"score":0.2761000096797943},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.27140000462532043}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.24120","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24120","pdf_url":"https://arxiv.org/pdf/2610.24120","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.2610.24120","doi":"https://doi.org/10.48550/arxiv.2610.24120","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.24120","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.24120","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24120","pdf_url":"https://arxiv.org/pdf/2610.24120","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222995324.pdf","grobid_xml":"https://content.openalex.org/works/W7222995324.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1990960441","https://openalex.org/W2029236081","https://openalex.org/W2040661328","https://openalex.org/W2045184478","https://openalex.org/W2075500376","https://openalex.org/W2224455529","https://openalex.org/W2611041228","https://openalex.org/W2798666872","https://openalex.org/W2963338039","https://openalex.org/W3110968703","https://openalex.org/W3183170542","https://openalex.org/W3208214335"],"related_works":["https://openalex.org/W3023870404","https://openalex.org/W4393217873","https://openalex.org/W2611041228","https://openalex.org/W2963288699","https://openalex.org/W3164918614","https://openalex.org/W2963074707","https://openalex.org/W4220840093","https://openalex.org/W7204449692","https://openalex.org/W3142892725","https://openalex.org/W2954698242"],"abstract_inverted_index":{"Let":[0,13],"$R$":[1,63],"be":[2,17,35,74],"a":[3,9,44],"unital":[4],"commutative":[5],"ring":[6],"and":[7,15,22,31,54,64],"$X$":[8,27,65],"partially":[10],"ordered":[11],"set.":[12],"$FI(X,R)$":[14],"$I(X,R)$":[16],"the":[18,23,36,39,47,67],"finitary":[19],"incidence":[20,24],"algebra":[21,49,72],"module":[25],"of":[26,38,46,50,52,69],"over":[28],"$R$,":[29],"respectively,":[30],"let":[32],"$D(X,R)=FI(X,R)\\oplus":[33],"I(X,R)$":[34],"idealization":[37],"$FI(X,R)$-bimodule":[40],"$I(X,R)$.":[41],"We":[42],"give":[43],"description":[45,68],"Lie":[48,71],"derivations":[51],"$D(X,R)$":[53],"also":[55],"provide":[56],"some":[57],"necessary":[58],"or":[59],"sufficient":[60],"conditions":[61],"on":[62],"for":[66],"this":[70],"to":[73],"simpler.":[75]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
