{"id":"https://openalex.org/W4415436620","doi":"https://doi.org/10.37193/cjm.2025.03.05","title":"Naturally ordered transformation semigroups preserving an equivalence relation on an invariant set","display_name":"Naturally ordered transformation semigroups preserving an equivalence relation on an invariant set","publication_year":2025,"publication_date":"2025-03-06","ids":{"openalex":"https://openalex.org/W4415436620","doi":"https://doi.org/10.37193/cjm.2025.03.05"},"language":"en","primary_location":{"id":"doi:10.37193/cjm.2025.03.05","doi":"https://doi.org/10.37193/cjm.2025.03.05","is_oa":true,"landing_page_url":"https://doi.org/10.37193/cjm.2025.03.05","pdf_url":"https://doi.org/10.37193/cjm.2025.03.05","source":{"id":"https://openalex.org/S14240099","display_name":"Carpathian Journal of Mathematics","issn_l":"1584-2851","issn":["1584-2851","1843-4401"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","norway-1","poland-40","russia-white-list-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carpathian Journal of Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4415436620"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.37193/cjm.2025.03.05","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056008627","display_name":"Ekkachai Laysirikul","orcid":"https://orcid.org/0000-0002-7079-0429","observed_orcids":["https://orcid.org/0000-0002-7079-0429"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"EKKACHAI LAYSIRIKUL","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092276570","display_name":"Kitsanachai Sripon","orcid":"https://orcid.org/0009-0007-4538-6639","observed_orcids":["https://orcid.org/0009-0007-4538-6639"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"KITSANACHAI SRIPON","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054705881","display_name":"Yanisa Chaiya","orcid":"https://orcid.org/0000-0002-7119-2658","observed_orcids":["https://orcid.org/0000-0002-7119-2658","https://orcid.org/0000-0002-6623-2619"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"YANISA CHAIYA","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":"673","last_page":"685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9961000084877014,"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":0.9961000084877014,"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":0.00139999995008111,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.0010000000474974513,"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/transformation-semigroups","display_name":"transformation semigroups","score":0.890999972820282},{"id":"https://openalex.org/keywords/full-transformation-semigroup","display_name":"full transformation semigroup","score":0.8640000224113464},{"id":"https://openalex.org/keywords/natural-partial-order","display_name":"natural partial order","score":0.9369999766349792},{"id":"https://openalex.org/keywords/equivalence-relations","display_name":"equivalence relations","score":0.8360000252723694},{"id":"https://openalex.org/keywords/invariant-sets","display_name":"invariant sets","score":0.9240000247955322},{"id":"https://openalex.org/keywords/subsemigroups","display_name":"subsemigroups","score":0.8960000276565552},{"id":"https://openalex.org/keywords/minimal-elements","display_name":"minimal elements","score":0.828000009059906},{"id":"https://openalex.org/keywords/maximal-elements","display_name":"maximal elements","score":0.9639999866485596}],"concepts":[{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.8575999736785889},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8392000198364258},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7221999764442444},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6543999910354614},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5741999745368958},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5327000021934509},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4348999857902527},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42660000920295715},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4198000133037567},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C196773441","wikidata":"https://www.wikidata.org/wiki/Q1475294","display_name":"Maximal element","level":3,"score":0.38909998536109924},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C34459055","wikidata":"https://www.wikidata.org/wiki/Q256151","display_name":"Matrix equivalence","level":4,"score":0.2632000148296356},{"id":"https://openalex.org/C2985459651","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Ordered set","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37193/cjm.2025.03.05","doi":"https://doi.org/10.37193/cjm.2025.03.05","is_oa":true,"landing_page_url":"https://doi.org/10.37193/cjm.2025.03.05","pdf_url":"https://doi.org/10.37193/cjm.2025.03.05","source":{"id":"https://openalex.org/S14240099","display_name":"Carpathian Journal of Mathematics","issn_l":"1584-2851","issn":["1584-2851","1843-4401"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","norway-1","poland-40","russia-white-list-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carpathian Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37193/cjm.2025.03.05","doi":"https://doi.org/10.37193/cjm.2025.03.05","is_oa":true,"landing_page_url":"https://doi.org/10.37193/cjm.2025.03.05","pdf_url":"https://doi.org/10.37193/cjm.2025.03.05","source":{"id":"https://openalex.org/S14240099","display_name":"Carpathian Journal of Mathematics","issn_l":"1584-2851","issn":["1584-2851","1843-4401"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","norway-1","poland-40","russia-white-list-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Carpathian Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415436620.pdf","grobid_xml":"https://content.openalex.org/works/W4415436620.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2015721883","https://openalex.org/W4393220365","https://openalex.org/W2048002508","https://openalex.org/W7150184785","https://openalex.org/W2027039467","https://openalex.org/W2015641760","https://openalex.org/W2784862883","https://openalex.org/W2093483709","https://openalex.org/W2068020816","https://openalex.org/W2891719785"],"abstract_inverted_index":{"For":[0],"a":[1,15,52,61],"nonempty":[2,16],"set":[3,32],"X,":[4,28],"let":[5],"T(X)":[6],"represent":[7],"the":[8,31,64,73],"full":[9],"transformation":[10],"semigroup":[11],"on":[12,27,68],"X.":[13],"Given":[14],"subset":[17],"Y":[18],"of":[19,54,63],"X":[20],"and":[21,83],"an":[22],"equivalence":[23],"relation":[24],"E":[25,42],"defined":[26],"we":[29,59,71],"consider":[30],"S_E(X,Y)":[33,50],"=":[34],"{\u03b1":[35],"\u2208T(X)":[36],":":[37],"\u2200x,y":[38],"\u2208":[39,41,45,47],"Y,(x,y)":[40],"\u21d2":[43],"(x\u03b1,y\u03b1)":[44],"E,x\u03b1,y\u03b1":[46],"Y}.":[48],"Then":[49],"is":[51],"subsemigroup":[53],"T(X).":[55],"In":[56],"this":[57],"paper,":[58],"provide":[60],"characterization":[62],"natural":[65],"partial":[66],"order":[67],"S_E(X,Y).":[69],"Moreover,":[70],"investigate":[72],"elements":[74],"within":[75],"S_E(X,Y":[76],")":[77],"which":[78],"are":[79],"minimal,":[80],"maximal":[81],"right-compatible,":[82],"left-compatible":[84],"with":[85],"respect":[86],"to":[87],"such":[88],"order.":[89]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2025-10-23T00:00:00"}
