{"id":"https://openalex.org/W2070730822","doi":"https://doi.org/10.1142/s0218196707003792","title":"ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\\mathcal{I}_{X}^{\\ast}$","display_name":"ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\\mathcal{I}_{X}^{\\ast}$","publication_year":2007,"publication_date":"2007-05-01","ids":{"openalex":"https://openalex.org/W2070730822","doi":"https://doi.org/10.1142/s0218196707003792","mag":"2070730822"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196707003792","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196707003792","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/A5047117906","display_name":"Victor Maltcev","orcid":null},"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"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["GB","SK"],"is_corresponding":true,"raw_author_name":"VICTOR MALTCEV","raw_affiliation_strings":["Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047117906"],"corresponding_institution_ids":["https://openalex.org/I16835326","https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":1.3076,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.77708119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"03","first_page":"567","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9997000098228455,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9987000226974487,"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":0.8417297601699829},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.7464109659194946},{"id":"https://openalex.org/keywords/inverse-semigroup","display_name":"Inverse semigroup","score":0.6353364586830139},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6057033538818359},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5516484975814819},{"id":"https://openalex.org/keywords/inverse-element","display_name":"Inverse element","score":0.5441847443580627},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.5273253321647644},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.5044056177139282},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.4960425794124603},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.4909665882587433},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4821767210960388},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34283900260925293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32888320088386536},{"id":"https://openalex.org/keywords/special-classes-of-semigroups","display_name":"Special classes of semigroups","score":0.08675700426101685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06838595867156982}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8417297601699829},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7464109659194946},{"id":"https://openalex.org/C2778508345","wikidata":"https://www.wikidata.org/wiki/Q3022118","display_name":"Inverse semigroup","level":3,"score":0.6353364586830139},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6057033538818359},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5516484975814819},{"id":"https://openalex.org/C105245699","wikidata":"https://www.wikidata.org/wiki/Q338057","display_name":"Inverse element","level":4,"score":0.5441847443580627},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.5273253321647644},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.5044056177139282},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.4960425794124603},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.4909665882587433},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4821767210960388},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34283900260925293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32888320088386536},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.08675700426101685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06838595867156982},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C112698675","wikidata":"https://www.wikidata.org/wiki/Q37038","display_name":"Advertising","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196707003792","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196707003792","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":12,"referenced_works":["https://openalex.org/W1487875360","https://openalex.org/W1507686949","https://openalex.org/W1982898031","https://openalex.org/W2006683826","https://openalex.org/W2019497911","https://openalex.org/W2027662173","https://openalex.org/W2051808789","https://openalex.org/W2086681482","https://openalex.org/W2088306712","https://openalex.org/W2105619816","https://openalex.org/W2117205980","https://openalex.org/W4251535942"],"related_works":["https://openalex.org/W51936586","https://openalex.org/W2129046713","https://openalex.org/W2012328641","https://openalex.org/W2075298753","https://openalex.org/W2147082041","https://openalex.org/W2007611208","https://openalex.org/W2326730740","https://openalex.org/W2930972157","https://openalex.org/W2084543966","https://openalex.org/W3167030359"],"abstract_inverted_index":{"We":[0,20,32,54,66],"construct":[1,109],"the":[2,10,58,71,76,126],"inverse":[3,13,73,77],"partition":[4,78],"semigroup[Formula:":[5],"see":[6,15,30,39,48,62,100,105,113,117,124,128,132],"text],":[7,16,101,118,125,133],"isomorphic":[8],"to":[9,69,88,103],"dual":[11],"symmetric":[12,72],"monoid[Formula:":[14],"introduced":[17],"in":[18,135],"[6].":[19],"give":[21],"a":[22,43,92],"convenient":[23],"geometric":[24],"illustration":[25],"for":[26,46],"elements":[27],"of":[28,37,60,98,115,122,130],"[Formula:":[29,38,47,61,99,104,112,116,123,127,131],"text].":[31,106],"describe":[33],"all":[34,57],"maximal":[35],"subsemigroups":[36],"text]":[40,49,63],"and":[41],"find":[42],"generating":[44],"set":[45],"when":[50],"X":[51],"is":[52,91,120],"finite.":[53],"prove":[55],"that":[56],"automorphisms":[59],"are":[64],"inner.":[65],"show":[67],"how":[68],"embed":[70],"semigroup":[74],"into":[75],"one.":[79],"For":[80],"finite":[81],"sets":[82],"X,":[83],"we":[84,108],"establish":[85],"that,":[86],"up":[87],"equivalence,":[89],"there":[90],"unique":[93],"faithful":[94],"effective":[95],"transitive":[96],"representation":[97],"namely":[102],"Finally,":[107],"an":[110],"interesting":[111],"text]-cross-section":[114,129],"which":[119],"reminiscent":[121],"constructed":[134],"[4].":[136]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}