{"id":"https://openalex.org/W7131663177","doi":"https://doi.org/10.48550/arxiv.2602.22147","title":"Similitudes over fields with I^4=0","display_name":"Similitudes over fields with I^4=0","publication_year":2026,"publication_date":"2026-02-25","ids":{"openalex":"https://openalex.org/W7131663177","doi":"https://doi.org/10.48550/arxiv.2602.22147"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2602.22147","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.22147","pdf_url":"https://arxiv.org/pdf/2602.22147","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.22147","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125684095","display_name":"M. Archita","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Archita, M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018900182","display_name":"Karim Johann\u00e8s Becher","orcid":"https://orcid.org/0000-0002-6197-594X","observed_orcids":["https://orcid.org/0000-0002-6197-594X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Becher, Karim Johannes","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":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/T11680","display_name":"Advanced Algebra and Geometry","score":0.8285999894142151,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.8285999894142151,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.13930000364780426,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.018400000408291817,"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/similitude","display_name":"similitude","score":0.6959999799728394},{"id":"https://openalex.org/keywords/r-equivalence","display_name":"R-equivalence","score":0.7649999856948853},{"id":"https://openalex.org/keywords/orthogonal-involutions","display_name":"orthogonal involutions","score":0.9549999833106995},{"id":"https://openalex.org/keywords/quadratic-forms","display_name":"quadratic forms","score":0.8980000019073486},{"id":"https://openalex.org/keywords/zero-divisors","display_name":"zero divisors","score":0.5249999761581421},{"id":"https://openalex.org/keywords/characteristic-not-2","display_name":"characteristic not 2","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7332000136375427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6536999940872192},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5457000136375427},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5264000296592712},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.5232999920845032},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.2596000134944916}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.22147","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.22147","pdf_url":"https://arxiv.org/pdf/2602.22147","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2602.22147","doi":"https://doi.org/10.48550/arxiv.2602.22147","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.22147","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.22147","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.22147","pdf_url":"https://arxiv.org/pdf/2602.22147","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7131663177.pdf","grobid_xml":"https://content.openalex.org/works/W7131663177.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,45],"article":[1],"studies":[2],"the":[3,9,21,70,73,80],"set":[4],"of":[5,8,11,15,20,30,49,54,58,62],"R-equivalence":[6],"classes":[7],"group":[10],"proper":[12],"projective":[13],"similitudes":[14],"an":[16],"algebra":[17],"with":[18],"involution":[19],"first":[22],"kind.":[23],"The":[24],"main":[25],"results":[26,61],"concern":[27],"base":[28,74],"fields":[29,48],"characteristic":[31],"different":[32],"from":[33],"2":[34],"over":[35],"which":[36],"every":[37],"9-dimensional":[38],"quadratic":[39],"form":[40],"has":[41],"a":[42],"nontrivial":[43],"zero.":[44],"includes":[46],"function":[47],"p-adic":[50],"curves":[51],"and":[52,64],"extensions":[53],"transcendence":[55],"degree":[56],"3":[57],"C.":[59],"Main":[60],"[28]":[63],"[29]":[65],"are":[66],"extended":[67],"by":[68],"relaxing":[69],"condition":[71],"on":[72,79],"field":[75],"as":[76,78],"well":[77],"Clifford":[81],"invariant":[82],"for":[83],"orthogonal":[84],"involutions.":[85]},"counts_by_year":[],"updated_date":"2026-09-25T08:18:29.962427","created_date":"2026-02-27T00:00:00"}