{"id":"https://openalex.org/W4416951591","doi":"https://doi.org/10.1090/mcom/4136","title":"Computing finite index congruences of finitely presented semigroups and monoids","display_name":"Computing finite index congruences of finitely presented semigroups and monoids","publication_year":2025,"publication_date":"2025-12-03","ids":{"openalex":"https://openalex.org/W4416951591","doi":"https://doi.org/10.1090/mcom/4136"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4136","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4136","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of 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/A5052197207","display_name":"Marina Anagnostopoulou\u2010Merkouri","orcid":"https://orcid.org/0009-0008-3808-4090"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marina Anagnostopoulou-Merkouri","raw_affiliation_strings":["School of Mathematics, University of Bristol, Fry Building, Woodland Rd, Bristol BS8 1UG, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bristol, Fry Building, Woodland Rd, Bristol BS8 1UG, United Kingdom","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062185112","display_name":"Reinis Cirpons","orcid":"https://orcid.org/0000-0001-7238-1576"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Reinis Cirpons","raw_affiliation_strings":["School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070323843","display_name":"James D. Mitchell","orcid":"https://orcid.org/0000-0002-5489-1617"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Mitchell","raw_affiliation_strings":["School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016430230","display_name":"Maria Tsalakou","orcid":"https://orcid.org/0000-0002-5628-2532"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Maria Tsalakou","raw_affiliation_strings":["School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St. Andrews, Mathematical Institute, North Haugh, St. Andrews, Fife KY16 9SS, United Kingdom","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28844065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"362","first_page":"3101","last_page":"3172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.7317000031471252,"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":0.7317000031471252,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.07970000058412552,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.046799998730421066,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.8299999833106995},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6906999945640564},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.598800003528595},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5724999904632568},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.5199999809265137},{"id":"https://openalex.org/keywords/krohn\u2013rhodes-theory","display_name":"Krohn\u2013Rhodes theory","score":0.4934000074863434},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.46230000257492065},{"id":"https://openalex.org/keywords/regular-semigroup","display_name":"Regular semigroup","score":0.44290000200271606}],"concepts":[{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.8299999833106995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8003000020980835},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6906999945640564},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.598800003528595},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5724999904632568},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.5199999809265137},{"id":"https://openalex.org/C30397308","wikidata":"https://www.wikidata.org/wiki/Q6438788","display_name":"Krohn\u2013Rhodes theory","level":4,"score":0.4934000074863434},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.46230000257492065},{"id":"https://openalex.org/C2776380127","wikidata":"https://www.wikidata.org/wiki/Q3022119","display_name":"Regular semigroup","level":4,"score":0.44290000200271606},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.42579999566078186},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4016999900341034},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.39410001039505005},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.3797000050544739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3716000020503998},{"id":"https://openalex.org/C2778508345","wikidata":"https://www.wikidata.org/wiki/Q3022118","display_name":"Inverse semigroup","level":3,"score":0.35260000824928284},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3206000030040741},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3037000000476837},{"id":"https://openalex.org/C58249144","wikidata":"https://www.wikidata.org/wiki/Q7597316","display_name":"Stallings theorem about ends of groups","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4136","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4136","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G935284534","display_name":"Maths DTP 2020 University of St Andrews","funder_award_id":"EP/V520123/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W258303743","https://openalex.org/W370468244","https://openalex.org/W567605243","https://openalex.org/W618980177","https://openalex.org/W1487875360","https://openalex.org/W1770411861","https://openalex.org/W1968491688","https://openalex.org/W1977607907","https://openalex.org/W1979501573","https://openalex.org/W1998095289","https://openalex.org/W2007572576","https://openalex.org/W2022132320","https://openalex.org/W2036318904","https://openalex.org/W2045417459","https://openalex.org/W2048063555","https://openalex.org/W2050134513","https://openalex.org/W2070730822","https://openalex.org/W2076654015","https://openalex.org/W2124685555","https://openalex.org/W2145062905","https://openalex.org/W2153126460","https://openalex.org/W2164766003","https://openalex.org/W2168316830","https://openalex.org/W2255021125","https://openalex.org/W2329945821","https://openalex.org/W2332968737","https://openalex.org/W2488025056","https://openalex.org/W2782743124","https://openalex.org/W2890232039","https://openalex.org/W2891750087","https://openalex.org/W2899013134","https://openalex.org/W2917234713","https://openalex.org/W2963350178","https://openalex.org/W2963631886","https://openalex.org/W2964218164","https://openalex.org/W3000680887","https://openalex.org/W3093166613","https://openalex.org/W3207565466","https://openalex.org/W3207633052","https://openalex.org/W3217779382","https://openalex.org/W4206142531","https://openalex.org/W4236837559","https://openalex.org/W4248336084","https://openalex.org/W4254266488","https://openalex.org/W4281846588","https://openalex.org/W4384207748","https://openalex.org/W4391917755","https://openalex.org/W4396602152"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,86,132,140],"paper,":[2],"we":[3],"describe":[4],"an":[5,27],"algorithm":[6,29,51,59,69,87,175],"for":[7,60,114,168,198],"computing":[8],"the":[9,31,41,62,72,102,118,128,136,145,173,179],"left,":[10],"right,":[11],"or":[12,20,35],"2-sided":[13],"congruences":[14,63,122],"of":[15,55,64,80,85,104,111,120,131,135],"a":[16,53,65,109],"finitely":[17,23,32],"presented":[18,33,44],"semigroup":[19,34],"monoid":[21,36],"with":[22,45],"many":[24],"classes,":[25],"and":[26,76,108,152,172,200,206,217],"alternative":[28],"when":[30],"is":[37,52,176],"finite.":[38],"We":[39,97],"compare":[40],"two":[42],"algorithms":[43,137],"existing":[46],"algorithmsand":[47],"implementations.":[48],"The":[49,67],"first":[50,129,174],"generalization":[54],"Sims\u2019":[56],"low-index":[57],"subgroup":[58],"finding":[61,78],"monoid.":[66],"second":[68],"involves":[70],"determining":[71],"distinct":[73],"principal":[74,121],"congruences,":[75],"then":[77],"all":[79],"their":[81],"possible":[82],"joins.":[83],"Variations":[84],"have":[88],"been":[89],"suggested":[90],"in":[91,139,144,178,207],"numerous":[92,95],"contexts":[93],"by":[94],"authors.":[96],"show":[98],"how":[99],"to":[100,116],"utilize":[101],"theory":[103],"relative":[105],"Green\u2019s":[106],"relations,":[107],"version":[110,154,203],"Schreier\u2019s":[112],"Lemma":[113],"monoids,":[115],"reduce":[117],"number":[119],"that":[123],"must":[124],"be":[125],"generated":[126],"as":[127],"step":[130],"approach.":[133],"Both":[134],"described":[138],"paper":[141],"are":[142],"implemented":[143],"GAP":[146,148,169],"[":[147,165,194,220],"-":[149],"groups,":[150],"algorithms,":[151],"programming,":[153],"5.5.4":[155],",":[156,170,202,224],"2025]":[157],"package":[158,167],"Semigroups":[159,166],"(see":[160,183,212],"J.":[161,186,188,213],"Mitchell":[162],"et":[163],"al.":[164],"2025]),":[171],"available":[177],"C++":[180],"library":[181,197],"libsemigroups":[182,195,221],"R.":[184],"Cirpons,":[185],"Edwards,":[187],"Mitchell,":[189,214],"M.":[190,192,218],"Tsalakou,":[191],"Whyte":[193],"c++":[196],"semigroups":[199],"monoids":[201],"1.1.0,":[204],"2025])":[205],"its":[208],"Python":[209],"bindings":[210],"libsemigroups_pybind11":[211],"C.":[215],"Nagpal,":[216],"Tsalakou":[219],"pybind11":[222],"v0.10.1":[223],"2023]).":[225]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-12-03T00:00:00"}