{"id":"https://openalex.org/W2039843463","doi":"https://doi.org/10.1142/s0218196705002414","title":"SOLVABLE MONOIDS WITH COMMUTING IDEMPOTENTS","display_name":"SOLVABLE MONOIDS WITH COMMUTING IDEMPOTENTS","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W2039843463","doi":"https://doi.org/10.1142/s0218196705002414","mag":"2039843463"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196705002414","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196705002414","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/A5002542775","display_name":"Manuel Delgado","orcid":"https://orcid.org/0000-0002-1935-9908"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"MANUEL DELGADO","raw_affiliation_strings":["Centro de Matem\u00e1tica, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal"],"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065470124","display_name":"V\u00edtor H. Fernandes","orcid":"https://orcid.org/0000-0003-1057-4975"},"institutions":[{"id":"https://openalex.org/I83558840","display_name":"Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89","country_code":"PT","type":"education","lineage":["https://openalex.org/I83558840"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"V\u00cdTOR H. FERNANDES","raw_affiliation_strings":["C.A.U.L., Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal","Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516 Caparica, Portugal"],"affiliations":[{"raw_affiliation_string":"C.A.U.L., Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal","institution_ids":[]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516 Caparica, Portugal","institution_ids":["https://openalex.org/I83558840"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002542775"],"corresponding_institution_ids":["https://openalex.org/I182534213"],"apc_list":null,"apc_paid":null,"fwci":0.6733,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7124616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"03","first_page":"547","last_page":"570"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.9043530821800232},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.7859241962432861},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.752517819404602},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.6528509259223938},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.49944591522216797},{"id":"https://openalex.org/keywords/solvable-group","display_name":"Solvable group","score":0.46553316712379456},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.44535404443740845},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4348723590373993},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4300367832183838},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38997071981430054},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33506691455841064}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9043530821800232},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7859241962432861},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.752517819404602},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.6528509259223938},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.49944591522216797},{"id":"https://openalex.org/C186746360","wikidata":"https://www.wikidata.org/wiki/Q759832","display_name":"Solvable group","level":3,"score":0.46553316712379456},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.44535404443740845},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4348723590373993},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4300367832183838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38997071981430054},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33506691455841064},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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":5,"locations":[{"id":"doi:10.1142/s0218196705002414","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196705002414","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:CiteSeerX.psu:10.1.1.908.3129","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.908.3129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://run.unl.pt///bitstream/10362/5518/1/Fernandes_2005.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.908.3797","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.908.3797","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Vitor_Fernandes/publication/220169583_Solvable_Monoids_with_Commuting_Idempotents/links/0deec5240ac9fcfed2000000.pdf?origin%3Dpublication_detail","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.910.2178","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.910.2178","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2005/7_05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.912.1539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.912.1539","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Vitor_Fernandes/publication/220169583_Solvable_Monoids_with_Commuting_Idempotents/links/0deec5240ac9fcfed2000000.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323424","display_name":"Universidade de Lisboa","ror":"https://ror.org/01c27hj86"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320335191","display_name":"Centro de Matem\u00e1tica Universidade do Porto","ror":"https://ror.org/043pwc612"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1487875360","https://openalex.org/W1533648993","https://openalex.org/W1543877612","https://openalex.org/W1600140231","https://openalex.org/W1804715396","https://openalex.org/W1872780986","https://openalex.org/W1976644338","https://openalex.org/W1980318512","https://openalex.org/W1981684679","https://openalex.org/W1996281160","https://openalex.org/W2002083342","https://openalex.org/W2015438020","https://openalex.org/W2025481592","https://openalex.org/W2034386479","https://openalex.org/W2034979418","https://openalex.org/W2035689363","https://openalex.org/W2038638040","https://openalex.org/W2046268252","https://openalex.org/W2063858816","https://openalex.org/W2077412768","https://openalex.org/W2085717272","https://openalex.org/W2165066480","https://openalex.org/W2165377501","https://openalex.org/W2167010548","https://openalex.org/W2798528163","https://openalex.org/W4299651338"],"related_works":["https://openalex.org/W4380433168","https://openalex.org/W2257057625","https://openalex.org/W4220976029","https://openalex.org/W3169949799","https://openalex.org/W1616996558","https://openalex.org/W2363874211","https://openalex.org/W2064501073","https://openalex.org/W2183076253","https://openalex.org/W2098553512","https://openalex.org/W2026105624"],"abstract_inverted_index":{"The":[0],"notion":[1,11,26],"of":[2,5,12,15,24,27,43],"Abelian":[3,44],"kernel":[4],"a":[6,16],"finite":[7,17,61],"monoid":[8],"extends":[9],"the":[10,25,37,41,48,52,60],"derived":[13],"subgroup":[14],"group.":[18],"In":[19],"this":[20,57,66],"line,":[21],"an":[22],"extension":[23],"solvable":[28],"group":[29],"to":[30],"monoids":[31,38,64],"is":[32],"quite":[33],"natural:":[34],"they":[35],"are":[36,68,73],"such":[39],"that":[40,59],"chain":[42],"kernels":[45],"ends":[46],"with":[47],"submonoid":[49],"generated":[50],"by":[51],"idempotents.":[53],"We":[54],"prove":[55],"in":[56],"paper":[58],"idempotent":[62],"commuting":[63],"satisfying":[65],"property":[67],"precisely":[69],"those":[70],"whose":[71],"subgroups":[72],"solvable.":[74]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}