{"id":"https://openalex.org/W2104632082","doi":"https://doi.org/10.1142/s0218196792000177","title":"A CONDITION GUARANTEEING COMMUTATIVITY","display_name":"A CONDITION GUARANTEEING COMMUTATIVITY","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2104632082","doi":"https://doi.org/10.1142/s0218196792000177","mag":"2104632082"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196792000177","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196792000177","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5079434052","display_name":"Irvin Roy Hentzel","orcid":null},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"IRVIN ROY HENTZEL","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA","Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA#TAB#","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010007087","display_name":"David P. Jacobs","orcid":"https://orcid.org/0000-0001-9409-0761"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.P. JACOBS","raw_affiliation_strings":["Department of Computer Science, Clemson University, Clemson, S.C. 29634\u20131906, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Clemson University, Clemson, S.C. 29634\u20131906, USA","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079434052"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":1.7021,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82162459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"02","issue":"03","first_page":"291","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.9688290357589722},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8777663707733154},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.8358511924743652},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.7136526107788086},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6058778166770935},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5993255376815796},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5129591822624207},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4544135332107544},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3644523322582245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06571927666664124},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.03742718696594238}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9688290357589722},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8777663707733154},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.8358511924743652},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.7136526107788086},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6058778166770935},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5993255376815796},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5129591822624207},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4544135332107544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3644523322582245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06571927666664124},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.03742718696594238},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196792000177","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196792000177","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:lib.dr.iastate.edu:math_pubs-1143","is_oa":false,"landing_page_url":"https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1143&amp;amp;context=math_pubs","pdf_url":null,"source":{"id":"https://openalex.org/S4377196104","display_name":"Iowa State University Digital Repository (Iowa State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173911158","host_organization_name":"Iowa State University","host_organization_lineage":["https://openalex.org/I173911158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Publications","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.7856","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7856","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.clemson.edu/~dpj/albertstuff/albertpapers/commutegen.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.7381","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.7381","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.clemson.edu/~dpj/albertstuff/albertpapers/commutegen.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W2587222766","https://openalex.org/W4389574038","https://openalex.org/W4387718369","https://openalex.org/W3014450817","https://openalex.org/W2104632082"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,6,32],"simple":[3],"characterization":[4,47],"for":[5],"nonassociative":[7],"algebra":[8,56],"[Formula:":[9,19],"see":[10,20],"text],":[11],"having":[12],"characteristic":[13,41],"\u22602,":[14],"to":[15],"be":[16],"commutative.":[17],"Namely,":[18],"text]":[21],"is":[22,29,43],"commutative":[23],"if":[24,27],"and":[25,48],"only":[26],"it":[28],"flexible":[30],"with":[31],"commuting":[33],"set":[34],"of":[35],"generators.":[36],"A":[37],"counterexample":[38,50],"shows":[39],"that":[40],"\u22602":[42],"necessary.":[44],"Both":[45],"the":[46,49,54],"were":[51],"discovered":[52],"using":[53],"computer":[55],"system":[57],"in":[58],"[2].":[59]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
