{"id":"https://openalex.org/W2037608487","doi":"https://doi.org/10.1016/0304-3975(88)90104-1","title":"Critical classes for the \u03b10-product","display_name":"Critical classes for the \u03b10-product","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2037608487","doi":"https://doi.org/10.1016/0304-3975(88)90104-1","mag":"2037608487"},"language":"en","primary_location":{"id":"doi:10.1016/0304-3975(88)90104-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0304-3975(88)90104-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","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/A5046647174","display_name":"P\u00e1l D\u00f6m\u00f6si","orcid":null},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"P\u00e1l D\u00f6m\u00f6si","raw_affiliation_strings":["Institute of Mathematics, L. Kossuth University, Debrecen, 4010 Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, L. Kossuth University, Debrecen, 4010 Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n \u00c9sik","raw_affiliation_strings":["Bolyai Institute, A. J\u00f3zsef University, Szeged, 6720 Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bolyai Institute, A. J\u00f3zsef University, Szeged, 6720 Hungary","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":0.5358,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63872832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"1","first_page":"17","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T10142","display_name":"Formal Methods in Verification","score":0.9973999857902527,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/product","display_name":"Product (mathematics)","score":0.6421414613723755},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6316275596618652},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5998963117599487},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5202092528343201},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5124638676643372},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.46746376156806946},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4534868597984314},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33529090881347656},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3303268849849701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3168376684188843},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23118886351585388},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.22523215413093567},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2073073387145996}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6421414613723755},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6316275596618652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5998963117599487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5202092528343201},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5124638676643372},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.46746376156806946},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4534868597984314},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33529090881347656},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3303268849849701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3168376684188843},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23118886351585388},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.22523215413093567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2073073387145996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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":1,"locations":[{"id":"doi:10.1016/0304-3975(88)90104-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0304-3975(88)90104-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1538941884","https://openalex.org/W1581140154","https://openalex.org/W2048810582"],"related_works":["https://openalex.org/W4237277701","https://openalex.org/W2121424666","https://openalex.org/W1587028174","https://openalex.org/W4301250310","https://openalex.org/W2055420561","https://openalex.org/W2067700950","https://openalex.org/W1669998927","https://openalex.org/W3162039195","https://openalex.org/W2071225893","https://openalex.org/W4250321999"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
