{"id":"https://openalex.org/W2148956539","doi":"https://doi.org/10.2178/jsl/1278682213","title":"Quantifier elimination in valued Ore modules","display_name":"Quantifier elimination in valued Ore modules","publication_year":2010,"publication_date":"2010-07-09","ids":{"openalex":"https://openalex.org/W2148956539","doi":"https://doi.org/10.2178/jsl/1278682213","mag":"2148956539"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1278682213","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682213","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/34251/1/Belair-Point2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041388160","display_name":"Luc B\u00e9lair","orcid":null},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Luc B\u00e9lair","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9 du Qu\u00e9bec-Uqam, Cp. 8888 Succ. Centre-Ville, Montr\u00e9al, Qu\u00e9bec, H3C 3P8, Canada. E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9 du Qu\u00e9bec-Uqam, Cp. 8888 Succ. Centre-Ville, Montr\u00e9al, Qu\u00e9bec, H3C 3P8, Canada. E-mail:","institution_ids":["https://openalex.org/I159129438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044413957","display_name":"Fran\u00e7oise Point","orcid":"https://orcid.org/0000-0003-1414-952X"},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]},{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["BE","CA"],"is_corresponding":true,"raw_author_name":"Fran\u00e7oise Point","raw_affiliation_strings":["Institut de Math\u00e9matique, Universit\u00e9 de M\u00f6ns, Le Pentagone 20, Place du Parc, B-7000 Mons, Belgium. E-mail:","Franc \u00b8oise Point, Institut de math\u00e9matique, Universit\u00e9 de Mons-Hainaut, Le Pen-tagone, 6, avenue du Champ de Mars, B-7000 Mons, Belgium","Senior Research Associate at the \"Fonds National de la Recherche Scientifique\". Luc B\u00e9lair, D\u00e9partment de math\u00e9matiques, Universit\u00e9 du Qu\u00e9bec-UQAM, C.P. 8888 succ. centre-ville, Montr\u00e9al, Qu\u00e9bec, H3C 3P8"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matique, Universit\u00e9 de M\u00f6ns, Le Pentagone 20, Place du Parc, B-7000 Mons, Belgium. E-mail:","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"Franc \u00b8oise Point, Institut de math\u00e9matique, Universit\u00e9 de Mons-Hainaut, Le Pen-tagone, 6, avenue du Champ de Mars, B-7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"Senior Research Associate at the \"Fonds National de la Recherche Scientifique\". Luc B\u00e9lair, D\u00e9partment de math\u00e9matiques, Universit\u00e9 du Qu\u00e9bec-UQAM, C.P. 8888 succ. centre-ville, Montr\u00e9al, Qu\u00e9bec, H3C 3P8","institution_ids":["https://openalex.org/I159129438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044413957"],"corresponding_institution_ids":["https://openalex.org/I130929987","https://openalex.org/I159129438"],"apc_list":null,"apc_paid":null,"fwci":0.3195,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64222751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"3","first_page":"1007","last_page":"1034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9969000220298767,"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/T10126","display_name":"Logic, programming, and type systems","score":0.995199978351593,"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/quantifier-elimination","display_name":"Quantifier elimination","score":0.9650886058807373},{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.6030445694923401},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5762397050857544},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.5426888465881348},{"id":"https://openalex.org/keywords/residue-field","display_name":"Residue field","score":0.4817640781402588},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4753962457180023},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.47199395298957825},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4235013425350189},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37422436475753784},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29649072885513306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2861558198928833},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1133127510547638},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08864894509315491}],"concepts":[{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.9650886058807373},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.6030445694923401},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5762397050857544},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.5426888465881348},{"id":"https://openalex.org/C2781025942","wikidata":"https://www.wikidata.org/wiki/Q7315530","display_name":"Residue field","level":3,"score":0.4817640781402588},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4753962457180023},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.47199395298957825},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4235013425350189},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37422436475753784},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29649072885513306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2861558198928833},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1133127510547638},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08864894509315491},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1278682213","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682213","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:www.archipel.uqam.ca:1390","is_oa":false,"landing_page_url":"http://www.archipel.uqam.ca/1390/1/jsl2010-WmodBP09-02-23.pdf","pdf_url":"http://www.archipel.uqam.ca/1390/1/jsl2010-WmodBP09-02-23.pdf","source":{"id":"https://openalex.org/S4306401005","display_name":"Archipelago (Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210093668","host_organization_name":"Quebec Intensive Silviculture Network","host_organization_lineage":["https://openalex.org/I4210093668"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article de revue scientifique"},{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/34251","is_oa":true,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/34251","pdf_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/34251/1/Belair-Point2.pdf","source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 75 (3), 1007-1034 (2010-09-01)","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1278682213","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1278682213","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/34251","is_oa":true,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/34251","pdf_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/34251/1/Belair-Point2.pdf","source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 75 (3), 1007-1034 (2010-09-01)","raw_type":"http://purl.org/coar/resource_type/c_6501"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2148956539.pdf","grobid_xml":"https://content.openalex.org/works/W2148956539.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W47144720","https://openalex.org/W161825626","https://openalex.org/W199556903","https://openalex.org/W205112229","https://openalex.org/W560358004","https://openalex.org/W1026721552","https://openalex.org/W1491837590","https://openalex.org/W1501220516","https://openalex.org/W1550331971","https://openalex.org/W1564272180","https://openalex.org/W1577003333","https://openalex.org/W1603468845","https://openalex.org/W1964811036","https://openalex.org/W1969433217","https://openalex.org/W1969964841","https://openalex.org/W2036911735","https://openalex.org/W2082371560","https://openalex.org/W2091741226","https://openalex.org/W2092230546","https://openalex.org/W2109388402","https://openalex.org/W2164702394","https://openalex.org/W2215180673","https://openalex.org/W2283058393","https://openalex.org/W2327816196","https://openalex.org/W2330548796","https://openalex.org/W2499747575","https://openalex.org/W2761494500","https://openalex.org/W2771303109","https://openalex.org/W3183392806","https://openalex.org/W4212769511","https://openalex.org/W4250950881","https://openalex.org/W4301168154","https://openalex.org/W6641514759"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W2798639752","https://openalex.org/W1524103539","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W1973527399","https://openalex.org/W71729059","https://openalex.org/W2068866297"],"abstract_inverted_index":{"Abstract":[0],"We":[1,60],"consider":[2],"valued":[3,13],"fields":[4],"with":[5,44,56],"a":[6,45,53,57],"distinguished":[7],"isometry":[8],"or":[9],"contractive":[10],"derivation":[11],"as":[12],"modules":[14],"over":[15],"the":[16,26,35,72],"Ore":[17],"ring":[18],"of":[19,47],"difference":[20],"operators.":[21],"Under":[22],"certain":[23],"assumptions":[24],"on":[25],"residue":[27],"field,":[28],"we":[29],"prove":[30,65],"quantifier":[31,62],"elimination":[32,63],"first":[33],"in":[34,40,52],"pure":[36],"module":[37],"language,":[38],"then":[39],"that":[41,66],"language":[42,55],"augmented":[43],"chain":[46],"additive":[48],"subgroups,":[49],"and":[50],"finally":[51],"two-sorted":[54],"valuation":[58],"map.":[59],"apply":[61],"to":[64],"these":[67],"structures":[68],"do":[69],"not":[70],"have":[71],"independence":[73],"property.":[74]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}