{"id":"https://openalex.org/W2020416879","doi":"https://doi.org/10.1142/s0218196792000074","title":"SOME PROPERTIES OF FINITELY DECIDABLE VARIETIES","display_name":"SOME PROPERTIES OF FINITELY DECIDABLE VARIETIES","publication_year":1992,"publication_date":"1992-03-01","ids":{"openalex":"https://openalex.org/W2020416879","doi":"https://doi.org/10.1142/s0218196792000074","mag":"2020416879"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196792000074","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196792000074","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/A5081757255","display_name":"Matthew Valeriote","orcid":"https://orcid.org/0000-0001-6568-7526"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"MATTHEW A. VALERIOTE","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, Canada","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078983016","display_name":"Ross Willard","orcid":"https://orcid.org/0000-0002-3297-0453"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"ROSS WILLARD","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081757255"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":null,"apc_paid":null,"fwci":1.9223,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85635755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"02","issue":"01","first_page":"89","last_page":"101"},"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/T11727","display_name":"Advanced Algebra and Logic","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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8836573958396912},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.8263781070709229},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6200396418571472},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6103203296661377},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.601824164390564},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4951869547367096},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48198217153549194},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.47222140431404114},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4460236132144928},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.442301481962204},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4283443093299866},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3667633533477783},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05873182415962219},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04743030667304993}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8836573958396912},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8263781070709229},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6200396418571472},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6103203296661377},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.601824164390564},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4951869547367096},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48198217153549194},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.47222140431404114},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4460236132144928},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.442301481962204},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4283443093299866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3667633533477783},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05873182415962219},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04743030667304993},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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:10.1142/s0218196792000074","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196792000074","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"},{"id":"pmh:oai:repository.cmu.edu:math-1448","is_oa":false,"landing_page_url":"http://repository.cmu.edu/math/449","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematical Sciences","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6479528","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1512669024","https://openalex.org/W1597575289","https://openalex.org/W2022101231","https://openalex.org/W2023648368","https://openalex.org/W2033603815"],"related_works":["https://openalex.org/W2331020993","https://openalex.org/W2972379433","https://openalex.org/W4383764068","https://openalex.org/W1481826604","https://openalex.org/W1797057780","https://openalex.org/W4302436802","https://openalex.org/W2145687427","https://openalex.org/W2951508299","https://openalex.org/W4372278520","https://openalex.org/W2046460098"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,25,75,87,99],"see":[2,26,76,88,100],"text]":[3,27,77,89,101],"be":[4],"a":[5,13],"variety":[6],"whose":[7],"class":[8],"of":[9,24,42,45,74],"finite":[10,21,70,93],"members":[11,73],"has":[12,59],"decidable":[14],"first-order":[15],"theory.":[16],"We":[17],"prove":[18],"that":[19,38,85],"each":[20],"member":[22],"A":[23,51],"satisfies":[28],"the":[29,39,69],"(3,":[30,33],"1)":[31],"and":[32,37,94],"2)":[34],"transfer":[35],"principles,":[36],"minimal":[40],"sets":[41],"prime":[43],"quotients":[44],"type":[46,96],"2":[47],"or":[48],"3":[49],"in":[50,67],"must":[52],"have":[53],"empty":[54],"tails.":[55],"The":[56,81],"first":[57],"result":[58,83],"already":[60],"been":[61],"used":[62],"by":[63],"J.":[64],"Jeong":[65],"[9]":[66],"characterizing":[68],"subdirectly":[71],"irreducible":[72],"with":[78],"nonabelian":[79],"monolith.":[80],"second":[82],"implies":[84],"if":[86],"is":[90,102],"also":[91],"locally":[92],"omits":[95],"1,":[97],"then":[98],"congruence":[103],"modular.":[104]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}