{"id":"https://openalex.org/W7223206930","doi":"https://doi.org/10.48550/arxiv.2610.29712","title":"On unit groups of purely infinite rings","display_name":"On unit groups of purely infinite rings","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223206930","doi":"https://doi.org/10.48550/arxiv.2610.29712"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.29712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29712","pdf_url":"https://arxiv.org/pdf/2610.29712","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/2610.29712","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036511181","display_name":"Friedrich Martin Schneider","orcid":"https://orcid.org/0000-0002-4126-2758","observed_orcids":["https://orcid.org/0000-0002-4126-2758"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Schneider, Friedrich Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5036511181"],"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.8003000020980835,"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":0.8003000020980835,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.14010000228881836,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.02070000022649765,"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/unit-groups","display_name":"unit groups","score":0.8619999885559082},{"id":"https://openalex.org/keywords/regular-rings","display_name":"regular rings","score":0.7419999837875366},{"id":"https://openalex.org/keywords/involutions","display_name":"involutions","score":0.9860000014305115},{"id":"https://openalex.org/keywords/geometric-group-theory","display_name":"geometric group theory","score":0.9539999961853027}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.8755000233650208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7907999753952026},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5889999866485596},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5651999711990356},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5248000025749207},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.462799996137619},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4507000148296356},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44130000472068787},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C559843788","wikidata":"https://www.wikidata.org/wiki/Q374268","display_name":"Infinite group","level":3,"score":0.4065000116825104},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35749998688697815},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3206000030040741},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C2780811992","wikidata":"https://www.wikidata.org/wiki/Q21083858","display_name":"Finitely generated group","level":3,"score":0.258899986743927}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.29712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29712","pdf_url":"https://arxiv.org/pdf/2610.29712","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.2610.29712","doi":"https://doi.org/10.48550/arxiv.2610.29712","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.29712","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:2610.29712","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29712","pdf_url":"https://arxiv.org/pdf/2610.29712","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/G2145371597","display_name":null,"funder_award_id":"Projektnummer 561178190","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5610728504","display_name":null,"funder_award_id":"561178190","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223206930.pdf","grobid_xml":"https://content.openalex.org/works/W7223206930.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4405768159","https://openalex.org/W7102405432"],"related_works":["https://openalex.org/W2289124626","https://openalex.org/W2503300163","https://openalex.org/W2007719931","https://openalex.org/W1544226492","https://openalex.org/W7010123184","https://openalex.org/W2033635699","https://openalex.org/W7102405432","https://openalex.org/W2333999943","https://openalex.org/W3208793318","https://openalex.org/W1555602574"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3,61,65,91],"unit":[4],"group":[5,103],"of":[6,18,48,54,64,77,88],"any":[7],"purely":[8],"infinite,":[9],"regular,":[10],"right":[11],"self-injective":[12],"ring":[13],"admits":[14],"a":[15,74],"universal":[16],"sequence":[17],"words":[19],"(thus":[20],"has":[21,28,39],"strong":[22,42],"distortion),":[23],"is":[24,32,73],"minimally":[25],"almost":[26],"periodic,":[27],"finite":[29],"involution":[30],"width,":[31],"verbally":[33,36],"simple":[34],"and":[35,38,98],"elliptic,":[37],"uncountable":[40],"uniform":[41],"cofinality.":[43],"These":[44],"findings":[45],"are":[46],"consequences":[47],"more":[49],"refined":[50],"structural":[51],"results,":[52],"some":[53,95],"which":[55],"provide":[56],"concrete":[57],"cardinal":[58],"estimates":[59],"involving":[60],"Goodearl--Boyle":[62],"dimension":[63],"ring.":[66],"A":[67],"central":[68],"ingredient":[69],"in":[70,81],"our":[71],"results":[72],"comprehensive":[75],"study":[76],"bounded":[78],"normal":[79],"generation,":[80],"particular":[82],"with":[83],"respect":[84],"to":[85,101],"certain":[86],"classes":[87],"involutions.":[89],"Along":[90],"way,":[92],"we":[93],"develop":[94],"abstract":[96],"methods":[97],"concepts":[99],"pertaining":[100],"geometric":[102],"theory.":[104]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-23T00:00:00"}
