{"id":"https://openalex.org/W2135981550","doi":"https://doi.org/10.1142/s0218196798000089","title":"Monoid Presentations and Associated Groupoids","display_name":"Monoid Presentations and Associated Groupoids","publication_year":1998,"publication_date":"1998-04-01","ids":{"openalex":"https://openalex.org/W2135981550","doi":"https://doi.org/10.1142/s0218196798000089","mag":"2135981550"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196798000089","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000089","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/A5010431445","display_name":"N. D. Gilbert","orcid":"https://orcid.org/0000-0002-7280-2753"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"N. D. Gilbert","raw_affiliation_strings":["Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland","Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland","institution_ids":["https://openalex.org/I32062511"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010431445"],"corresponding_institution_ids":["https://openalex.org/I32062511"],"apc_list":null,"apc_paid":null,"fwci":1.1145,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.77292503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"08","issue":"02","first_page":"141","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.996999979019165,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.996999979019165,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9714999794960022,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9603999853134155,"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/monoid","display_name":"Monoid","score":0.9579002857208252},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8510667085647583},{"id":"https://openalex.org/keywords/syntactic-monoid","display_name":"Syntactic monoid","score":0.6482971906661987},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5669901967048645},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5075053572654724},{"id":"https://openalex.org/keywords/presentation","display_name":"Presentation (obstetrics)","score":0.48669201135635376},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.4586408734321594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4498969614505768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33866533637046814},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.050085991621017456}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.9579002857208252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8510667085647583},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.6482971906661987},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5669901967048645},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5075053572654724},{"id":"https://openalex.org/C2777601897","wikidata":"https://www.wikidata.org/wiki/Q3409113","display_name":"Presentation (obstetrics)","level":2,"score":0.48669201135635376},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.4586408734321594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4498969614505768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33866533637046814},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.050085991621017456},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196798000089","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000089","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1977314998","https://openalex.org/W1978362621","https://openalex.org/W2015953802","https://openalex.org/W2058556657","https://openalex.org/W2164680691"],"related_works":["https://openalex.org/W51936586","https://openalex.org/W3161268522","https://openalex.org/W3143205136","https://openalex.org/W2071633178","https://openalex.org/W2971508078","https://openalex.org/W2038387119","https://openalex.org/W3201418638","https://openalex.org/W2090238248","https://openalex.org/W2079194245","https://openalex.org/W1991410416"],"abstract_inverted_index":{"We":[0,13,39],"consider":[1],"properties":[2],"of":[3,36,51,57],"a":[4,10,20,26,42],"2-complex":[5],"associated":[6],"by":[7],"Squier":[8],"to":[9,46],"monoid":[11,21,49],"presentation.":[12],"show":[14],"that":[15],"the":[16,33,37,55,58],"fundamental":[17,34,59],"groupoid":[18,60],"admits":[19],"structure,":[22],"and":[23,32,53],"we":[24],"establish":[25],"relationship":[27],"between":[28],"its":[29],"group":[30,35],"completion":[31],"2-complex.":[38],"also":[40],"treat":[41],"modified":[43],"complex,":[44],"due":[45],"Pride,":[47],"for":[48],"presentations":[50],"groups,":[52],"compute":[54],"structure":[56],"in":[61],"this":[62],"setting.":[63]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
