{"id":"https://openalex.org/W1585649433","doi":null,"title":"The algebraic theory of semigroups","display_name":"The algebraic theory of semigroups","publication_year":1964,"publication_date":"1964-01-01","ids":{"openalex":"https://openalex.org/W1585649433","mag":"1585649433"},"language":"en","primary_location":{"id":"pmh:oai:cds.cern.ch:2122265","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2122265","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"volume":null,"type":"article","indexed_in":[],"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/A5064470378","display_name":"A. H. Clifford","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. H. Clifford","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060696648","display_name":"G. B. Preston","orcid":"https://orcid.org/0000-0001-8322-631X","observed_orcids":["https://orcid.org/0000-0001-8322-631X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. B. Preston","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":70.0923,"has_fulltext":false,"cited_by_count":3639,"citation_normalized_percentile":{"value":1.0,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9980000257492065,"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":0.9980000257492065,"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":0.0005000000237487257,"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/T12504","display_name":"Mathematics and Applications","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semigroups","display_name":"semigroups","score":0.8859999775886536},{"id":"https://openalex.org/keywords/semigroup-structure","display_name":"semigroup structure","score":0.5709999799728394},{"id":"https://openalex.org/keywords/minimal-ideals","display_name":"minimal ideals","score":0.9739999771118164},{"id":"https://openalex.org/keywords/inverse-semigroups","display_name":"inverse semigroups","score":0.996999979019165},{"id":"https://openalex.org/keywords/simple-semigroups","display_name":"simple semigroups","score":0.9990000128746033},{"id":"https://openalex.org/keywords/semigroup-congruences","display_name":"semigroup congruences","score":0.9629999995231628},{"id":"https://openalex.org/keywords/free-products-with-amalgamation","display_name":"amalgamated free products","score":0.9599999785423279},{"id":"https://openalex.org/keywords/full-transformation-semigroup","display_name":"full transformation semigroup","score":0.8700000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.749751627445221},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.7037590742111206},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.6021918058395386},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.5978381037712097},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.5265108346939087},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.48277679085731506},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4802013635635376},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46381041407585144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09234514832496643},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09214890003204346},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:cds.cern.ch:2122265","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2122265","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:cds.cern.ch:2122294","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2122294","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:1585649433","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/ncid/BA10698104","pdf_url":null,"source":{"id":"https://openalex.org/S4306462811","display_name":"American Mathematical Society eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321506","host_organization_name":"Serbian Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321506"],"host_organization_lineage_names":["Serbian Mathematical Society"],"type":"ebook platform"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"American Mathematical Society eBooks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2010305014","https://openalex.org/W2048174543","https://openalex.org/W2330992228"],"related_works":["https://openalex.org/W599215897","https://openalex.org/W3127823229","https://openalex.org/W2505692471","https://openalex.org/W2315234012","https://openalex.org/W2313247219","https://openalex.org/W2153525410","https://openalex.org/W2148893152","https://openalex.org/W2131820100","https://openalex.org/W2120713972","https://openalex.org/W2087976348","https://openalex.org/W2036018689","https://openalex.org/W2015195314","https://openalex.org/W1994765311","https://openalex.org/W1598703908","https://openalex.org/W1594985246","https://openalex.org/W1532289288","https://openalex.org/W1529355630","https://openalex.org/W1523977407","https://openalex.org/W1518454564","https://openalex.org/W1487875360"],"abstract_inverted_index":{"This":[0],"book,":[1],"along":[2],"with":[3],"volume":[4,30],"I,":[5],"which":[6,70],"appeared":[7],"previously,":[8],"presents":[9],"a":[10,39,50,57,61,94,124,130,133,145],"survey":[11],"of":[12,18,35,56,69,81,84,93,99,109,113,121,123,129,138,141],"the":[13,33,54,64,82,142],"structure":[14],"and":[15,53,116],"representation":[16],"theory":[17,80,98,108,120,140],"semi":[19,40,43,46,51,58,87,103,114,125,148],"groups.":[20],"Volume":[21],"II":[22],"goes":[23],"more":[24,65],"deeply":[25],"than":[26],"was":[27],"possible":[28],"in":[29,38,60],"I":[31],"into":[32],"theories":[34],"minimal":[36],"ideals":[37],"group,":[41,52],"inverse":[42],"groups,":[44,47,104,115],"simple":[45],"congruences":[48,143],"on":[49,144],"embedding":[55],"group":[59,88,126],"group.":[62,149],"Among":[63],"important":[66],"recent":[67],"developments":[68],"an":[71,85],"extended":[72],"treatment":[73],"is":[74,136],"presented":[75],"are":[76],"B.":[77],"M.":[78,106],"Sain's":[79],"representations":[83,122],"arbitrary":[86],"by":[89,127],"partial":[90],"one-to-one":[91],"transformations":[92,128],"set,":[95],"L.":[96],"Redei's":[97],"finitely":[100],"generated":[101],"commutative":[102],"J.":[105,118],"Howie's":[107],"amalgamated":[110],"free":[111],"products":[112],"E.":[117],"Tully's":[119],"set.":[131],"Also":[132],"full":[134,146],"account":[135],"given":[137],"Malcev's":[139],"transformation":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":39},{"year":2021,"cited_by_count":73},{"year":2020,"cited_by_count":65},{"year":2019,"cited_by_count":69},{"year":2018,"cited_by_count":66},{"year":2017,"cited_by_count":59},{"year":2016,"cited_by_count":98},{"year":2015,"cited_by_count":91},{"year":2014,"cited_by_count":82},{"year":2013,"cited_by_count":97},{"year":2012,"cited_by_count":94}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}