{"id":"https://openalex.org/W2165485639","doi":"https://doi.org/10.1017/s0960129503004110","title":"Wheels \u2013 on division by zero","display_name":"Wheels \u2013 on division by zero","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2165485639","doi":"https://doi.org/10.1017/s0960129503004110","mag":"2165485639"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129503004110","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129503004110","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097177513","display_name":"JESPER CARLSTRM","orcid":null},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"JESPER CARLSTR\u00d6M","raw_affiliation_strings":["Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Swedenhttp://www.math.su.se/~jesper"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Swedenhttp://www.math.su.se/~jesper","institution_ids":["https://openalex.org/I161593684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5097177513"],"corresponding_institution_ids":["https://openalex.org/I161593684"],"apc_list":null,"apc_paid":null,"fwci":0.3459,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.65004044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"1","first_page":"143","last_page":"184"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9976000189781189,"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/semiring","display_name":"Semiring","score":0.925101637840271},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7487698197364807},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.7174795269966125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7022944092750549},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6885002851486206},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6494359970092773},{"id":"https://openalex.org/keywords/noncommutative-ring","display_name":"Noncommutative ring","score":0.6294772624969482},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.6280922293663025},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5984375476837158},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5753233432769775},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5294715166091919},{"id":"https://openalex.org/keywords/zero-divisor","display_name":"Zero divisor","score":0.47688180208206177},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.46462494134902954},{"id":"https://openalex.org/keywords/division-ring","display_name":"Division ring","score":0.4155217707157135},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3772520422935486},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15708202123641968},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15511804819107056},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09706106781959534},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.08730608224868774}],"concepts":[{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.925101637840271},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7487698197364807},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.7174795269966125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7022944092750549},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6885002851486206},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6494359970092773},{"id":"https://openalex.org/C125225535","wikidata":"https://www.wikidata.org/wiki/Q7049224","display_name":"Noncommutative ring","level":3,"score":0.6294772624969482},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6280922293663025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5984375476837158},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5753233432769775},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5294715166091919},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.47688180208206177},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.46462494134902954},{"id":"https://openalex.org/C31671303","wikidata":"https://www.wikidata.org/wiki/Q650741","display_name":"Division ring","level":3,"score":0.4155217707157135},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3772520422935486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15708202123641968},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15511804819107056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09706106781959534},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.08730608224868774},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129503004110","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129503004110","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W569543113","https://openalex.org/W604140817","https://openalex.org/W1491813684","https://openalex.org/W1565484361","https://openalex.org/W2023648368","https://openalex.org/W2049707341","https://openalex.org/W2059204568","https://openalex.org/W2078334802","https://openalex.org/W2079735866","https://openalex.org/W2143658255","https://openalex.org/W2493333586","https://openalex.org/W3127823229"],"related_works":["https://openalex.org/W2385206495","https://openalex.org/W3081026123","https://openalex.org/W1969278805","https://openalex.org/W2092302066","https://openalex.org/W2378656894","https://openalex.org/W1537695149","https://openalex.org/W2037769793","https://openalex.org/W2165485639","https://openalex.org/W2990493803","https://openalex.org/W2362497513"],"abstract_inverted_index":{"We":[0],"show":[1,71],"how":[2,83],"to":[3,33,70,81,89],"extend":[4],"any":[5,14,37,46],"commutative":[6,41,47,93],"ring":[7,42,48],"(or":[8,43,49],"semiring)":[9,50],"so":[10],"that":[11,72],"division":[12],"by":[13],"element,":[15],"including":[16],"0,":[17],"is,":[18],"in":[19],"a":[20,28,40,58,61],"sense,":[21],"possible.":[22],"The":[23,63],"resulting":[24],"structure":[25],"is":[26,39,69],"called":[27],"wheel.":[29,62],"Wheels":[30],"are":[31,78],"similar":[32],"rings,":[34],"but":[35],"of":[36,60,66],"wheel":[38],"semiring),":[44],"and":[45,80,95],"with":[51],"identity":[52],"can":[53],"be":[54],"described":[55],"as":[56],"such":[57],"subset":[59],"main":[64],"goal":[65],"this":[67],"paper":[68],"the":[73],"given":[74],"axioms":[75],"for":[76,86,92],"wheels":[77,87],"natural,":[79],"clarify":[82],"valid":[84,90],"identities":[85,91],"relate":[88],"rings":[94],"semirings.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2016-06-24T00:00:00"}