{"id":"https://openalex.org/W3200758510","doi":"https://doi.org/10.1142/s0218196721500570","title":"Relatively free dimonoids and bar-units","display_name":"Relatively free dimonoids and bar-units","publication_year":2021,"publication_date":"2021-09-15","ids":{"openalex":"https://openalex.org/W3200758510","doi":"https://doi.org/10.1142/s0218196721500570","mag":"3200758510"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721500570","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500570","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/A5075305118","display_name":"Anatolii V. Zhuchok","orcid":"https://orcid.org/0000-0002-4254-823X"},"institutions":[{"id":"https://openalex.org/I2800458533","display_name":"University of Luhansk","ror":"https://ror.org/040wb2y55","country_code":"UA","type":"education","lineage":["https://openalex.org/I2800458533"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Anatolii V. Zhuchok","raw_affiliation_strings":["Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk 92703, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk 92703, Ukraine","institution_ids":["https://openalex.org/I2800458533"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075305118"],"corresponding_institution_ids":["https://openalex.org/I2800458533"],"apc_list":null,"apc_paid":null,"fwci":1.8871,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84431978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"08","first_page":"1587","last_page":"1599"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"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/T10849","display_name":"Finite Group Theory Research","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9763000011444092,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7650164365768433},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.676716685295105},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6499664187431335},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.544714093208313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.539662778377533},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5068345665931702},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.4787180423736572},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3365101218223572},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1435689628124237},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10092654824256897},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08632883429527283}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7650164365768433},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.676716685295105},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6499664187431335},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.544714093208313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.539662778377533},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5068345665931702},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.4787180423736572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3365101218223572},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1435689628124237},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10092654824256897},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08632883429527283},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196721500570","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500570","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":22,"referenced_works":["https://openalex.org/W1594760941","https://openalex.org/W1608296274","https://openalex.org/W1965094798","https://openalex.org/W2073474730","https://openalex.org/W2074725228","https://openalex.org/W2093034190","https://openalex.org/W2094353103","https://openalex.org/W2096327836","https://openalex.org/W2108749950","https://openalex.org/W2304713449","https://openalex.org/W2345375171","https://openalex.org/W2461879753","https://openalex.org/W2529813863","https://openalex.org/W2583561580","https://openalex.org/W2911417308","https://openalex.org/W2923271311","https://openalex.org/W3081873691","https://openalex.org/W3099109303","https://openalex.org/W4214903855","https://openalex.org/W4241044228","https://openalex.org/W4243816536","https://openalex.org/W4255110905"],"related_works":["https://openalex.org/W2288263127","https://openalex.org/W2152992791","https://openalex.org/W2293067204","https://openalex.org/W2378598099","https://openalex.org/W1989546358","https://openalex.org/W2263979563","https://openalex.org/W2952617247","https://openalex.org/W2260669059","https://openalex.org/W3081200114","https://openalex.org/W2964093409"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,45,75],"devoted":[3],"to":[4,16,30,47,53,77,109],"the":[5,8,31,54,64,84,94,104,116,119,127],"study":[6],"of":[7,10,14,28,51,58,82,98,118],"problem":[9],"adjoining":[11,25],"a":[12,26,49,80,110,133],"set":[13,27,50,81],"bar-units":[15,29,52,83],"dimonoids.":[17],"We":[18,113],"give":[19],"necessary":[20],"and":[21,41,63,103,126],"sufficient":[22],"conditions":[23],"for":[24,132],"free":[32,55,65,85,95,105,120,128],"left":[33,86,121],"[Formula:":[34,60,66,87,100,106,122,129],"see":[35,39,61,67,88,92,101,107,123,130],"text]-dinilpotent":[36,89,124],"dimonoid":[37,57,90,97,125],"([Formula:":[38,91],"text]),":[40,93],"prove":[42],"that":[43,73],"it":[44,74],"impossible":[46,76],"adjoin":[48],"abelian":[56,96],"rank":[59,99],"text]":[62,102],"text]-dimonoid.":[68],"As":[69],"consequences,":[70],"we":[71],"establish":[72],"extend":[78],"by":[79],"text]-dimonoid":[108,131],"generalized":[111],"digroup.":[112],"also":[114],"count":[115],"cardinalities":[117],"finite":[134],"case.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}