{"id":"https://openalex.org/W2024801444","doi":"https://doi.org/10.1142/s0218196709005275","title":"REPRESENTING SUBDIRECT PRODUCT MONOIDS BY GRAPHS","display_name":"REPRESENTING SUBDIRECT PRODUCT MONOIDS BY GRAPHS","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2024801444","doi":"https://doi.org/10.1142/s0218196709005275","mag":"2024801444"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005275","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005275","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/A5031559202","display_name":"V\u00e1c\u0142av Koubek","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"V\u00c1CLAV KOUBEK","raw_affiliation_strings":["Department of Theoretical Comp. Sci and Math. Logic, The Faculty of Mathematics and Physics, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Theoretical Comp. Sci and Math. Logic, The Faculty of Mathematics and Physics, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"VOJT\u011aCH R\u00d6DL","raw_affiliation_strings":["Department of Mathematics, Emory University, Atlanta, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Emory University, Atlanta, USA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059308003","display_name":"Benjamin Shemmer","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BENJAMIN SHEMMER","raw_affiliation_strings":["Department of Mathematics, Emory University, Atlanta, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Emory University, Atlanta, USA","institution_ids":["https://openalex.org/I150468666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031559202"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08175669,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"05","first_page":"705","last_page":"721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9858999848365784,"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":0.9690999984741211,"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/mathematics","display_name":"Mathematics","score":0.8932417631149292},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.886325478553772},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.8575241565704346},{"id":"https://openalex.org/keywords/syntactic-monoid","display_name":"Syntactic monoid","score":0.6777739524841309},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.643022894859314},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.641139566898346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5925456881523132},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4999971389770508},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4334530532360077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8932417631149292},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.886325478553772},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.8575241565704346},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.6777739524841309},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.643022894859314},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.641139566898346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5925456881523132},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4999971389770508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4334530532360077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005275","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005275","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W240203132","https://openalex.org/W1529355630","https://openalex.org/W1532289288","https://openalex.org/W1979573322","https://openalex.org/W1991455246","https://openalex.org/W2008208442","https://openalex.org/W2012649246","https://openalex.org/W2034331627","https://openalex.org/W2137593033","https://openalex.org/W2315063369","https://openalex.org/W4234244339"],"related_works":["https://openalex.org/W4288245503","https://openalex.org/W2069341570","https://openalex.org/W4311190503","https://openalex.org/W4288099353","https://openalex.org/W2394465002","https://openalex.org/W3175664114","https://openalex.org/W2064977911","https://openalex.org/W1984472426","https://openalex.org/W4296381451","https://openalex.org/W2093569370"],"abstract_inverted_index":{"Hedrl\u00edn":[0],"and":[1,55,83,119],"Pultr":[2],"proved":[3],"that":[4],"for":[5,29,67,88],"any":[6],"monoid":[7,16,35,66,89],"M":[8,36],"there":[9],"exists":[10],"a":[11,21,26,30,39,60,63],"graph":[12,31,61],"G":[13],"with":[14,32,62],"endomorphism":[15,34,65],"isomorphic":[17],"to":[18,58],"M.":[19],"In":[20,73],"previous":[22],"paper,":[23,75],"we":[24,46,76],"give":[25],"construction":[27,82],"G(M)":[28],"prescribed":[33],"known":[37],"as":[38],"[Formula:":[40,79],"see":[41,80],"text]-graph.":[42],"Using":[43],"this":[44,74],"construction,":[45],"derived":[47],"bounds":[48,87],"on":[49],"the":[50,78,100,112],"minimum":[51],"number":[52],"of":[53,70,105,111],"vertices":[54],"edges":[56],"required":[57],"produce":[59],"given":[64],"various":[68],"classes":[69,90],"finite":[71],"monoids.":[72],"generalize":[77],"text]-graph":[81],"derive":[84],"several":[85],"new":[86],"not":[91],"handled":[92],"by":[93],"our":[94],"first":[95],"paper.":[96],"Among":[97],"these":[98],"are":[99],"so":[101],"called":[102],"\"strong":[103],"semilattices":[104],"C-semigroups\"":[106],"where":[107],"C":[108],"is":[109],"one":[110],"following:":[113],"Groups,":[114,116,118],"Abelian":[115],"Rectangular":[117],"completely":[120],"simple":[121],"semigroups.":[122]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}