{"id":"https://openalex.org/W3148149592","doi":"https://doi.org/10.3390/sym13040558","title":"Semigroups of Terms, Tree Languages, Menger Algebra of n-Ary Functions and Their Embedding Theorems","display_name":"Semigroups of Terms, Tree Languages, Menger Algebra of n-Ary Functions and Their Embedding Theorems","publication_year":2021,"publication_date":"2021-03-27","ids":{"openalex":"https://openalex.org/W3148149592","doi":"https://doi.org/10.3390/sym13040558","mag":"3148149592"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040558","pdf_url":"https://www.mdpi.com/2073-8994/13/4/558/pdf?version=1617937448","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/558/pdf?version=1617937448","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019595410","display_name":"Thodsaporn Kumduang","orcid":"https://orcid.org/0000-0001-9848-133X"},"institutions":[{"id":"https://openalex.org/I48076826","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25","country_code":"TH","type":"education","lineage":["https://openalex.org/I48076826"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Thodsaporn Kumduang","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"],"raw_orcid":"https://orcid.org/0000-0001-9848-133X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand","institution_ids":["https://openalex.org/I48076826"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064270698","display_name":"Sorasak Leeratanavalee","orcid":"https://orcid.org/0000-0001-8818-6134"},"institutions":[{"id":"https://openalex.org/I48076826","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25","country_code":"TH","type":"education","lineage":["https://openalex.org/I48076826"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Sorasak Leeratanavalee","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand","Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"],"raw_orcid":"https://orcid.org/0000-0001-8818-6134","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand","institution_ids":["https://openalex.org/I48076826"]},{"raw_affiliation_string":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand","institution_ids":["https://openalex.org/I48076826"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064270698"],"corresponding_institution_ids":["https://openalex.org/I48076826"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3627,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83373947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"558","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991999864578247,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9927999973297119,"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/semigroup","display_name":"Semigroup","score":0.77024245262146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7528952360153198},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5766423344612122},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5514793395996094},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5382352471351624},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5265422463417053},{"id":"https://openalex.org/keywords/special-classes-of-semigroups","display_name":"Special classes of semigroups","score":0.5024597644805908},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4962933659553528},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.48063722252845764},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.45296764373779297},{"id":"https://openalex.org/keywords/regular-semigroup","display_name":"Regular semigroup","score":0.4267953634262085},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3696088194847107},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34717628359794617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20637449622154236},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14076027274131775}],"concepts":[{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.77024245262146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7528952360153198},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5766423344612122},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5514793395996094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5382352471351624},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5265422463417053},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.5024597644805908},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4962933659553528},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.48063722252845764},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.45296764373779297},{"id":"https://openalex.org/C2776380127","wikidata":"https://www.wikidata.org/wiki/Q3022119","display_name":"Regular semigroup","level":4,"score":0.4267953634262085},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3696088194847107},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34717628359794617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20637449622154236},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14076027274131775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040558","pdf_url":"https://www.mdpi.com/2073-8994/13/4/558/pdf?version=1617937448","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1fd243fba1924cceaafe5089e4caf5ea","is_oa":true,"landing_page_url":"https://doaj.org/article/1fd243fba1924cceaafe5089e4caf5ea","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 4, p 558 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/558/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040558","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13040558","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040558","pdf_url":"https://www.mdpi.com/2073-8994/13/4/558/pdf?version=1617937448","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321529","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3148149592.pdf","grobid_xml":"https://content.openalex.org/works/W3148149592.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W163873943","https://openalex.org/W274948173","https://openalex.org/W906895073","https://openalex.org/W1600732101","https://openalex.org/W2008255303","https://openalex.org/W2021472669","https://openalex.org/W2025302603","https://openalex.org/W2026393859","https://openalex.org/W2038909626","https://openalex.org/W2261418557","https://openalex.org/W2322615891","https://openalex.org/W2413120492","https://openalex.org/W2614139145","https://openalex.org/W2751045755","https://openalex.org/W2782658005","https://openalex.org/W2807535918","https://openalex.org/W2884616187","https://openalex.org/W2911295106","https://openalex.org/W2951513082","https://openalex.org/W3005802460","https://openalex.org/W3023912471","https://openalex.org/W3098016023","https://openalex.org/W3098726882","https://openalex.org/W3116280671","https://openalex.org/W4391299389","https://openalex.org/W6624314090","https://openalex.org/W6636097822","https://openalex.org/W6700344130","https://openalex.org/W6747784972","https://openalex.org/W6752319645","https://openalex.org/W6753444016","https://openalex.org/W6808419989","https://openalex.org/W6861355486","https://openalex.org/W7035978327"],"related_works":["https://openalex.org/W4212828952","https://openalex.org/W4400653608","https://openalex.org/W2033701980","https://openalex.org/W262066018","https://openalex.org/W2361990078","https://openalex.org/W1965853409","https://openalex.org/W2963805867","https://openalex.org/W2892268807","https://openalex.org/W2762094349","https://openalex.org/W2403522523"],"abstract_inverted_index":{"The":[0],"concepts":[1],"of":[2,13,34,54,57,69,85,91,99,106,114,119,133],"terms":[3,35,47,115],"and":[4,20,36,48,63,88,103],"tree":[5,37,86],"languages":[6,87],"are":[7,71,78],"significant":[8],"tools":[9,42],"for":[10,43,130],"the":[11,41,81,89,95,104,112,117,127],"development":[12],"research":[14],"works":[15],"in":[16],"both":[17],"universal":[18],"algebra":[19,132],"theoretical":[21],"computer":[22],"science.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,74],"establish":[28],"a":[29,55,140],"strong":[30],"connection":[31],"between":[32,46],"semigroups":[33],"languages,":[38],"which":[39,135],"provides":[40],"studying":[44],"monomorphisms":[45,79],"generalized":[49,59,92,101,108],"hypersubstitutions.":[50],"A":[51],"novel":[52],"concept":[53],"seminearring":[56],"non-deterministic":[58,100,107],"hypersubstitutions":[60,93,102],"is":[61,122],"introduced":[62],"some":[64],"interesting":[65],"properties":[66],"among":[67],"subsets":[68],"its":[70],"provided.":[72],"Furthermore,":[73],"prove":[75],"that":[76],"there":[77],"from":[80],"power":[82,96],"diagonal":[83,97],"semigroup":[84,98],"monoid":[90,105],"to":[94,138],"hypersubstitutions,":[109],"respectively.":[110],"Finally,":[111],"representation":[113],"using":[116],"theory":[118],"n-ary":[120],"functions":[121],"defined.":[123],"We":[124],"then":[125],"present":[126],"Cayley\u2019s":[128],"theorem":[129],"Menger":[131],"terms,":[134],"allows":[136],"us":[137],"provide":[139],"concrete":[141],"example":[142],"via":[143],"full":[144],"transformation":[145],"semigroups.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2021-04-13T00:00:00"}