{"id":"https://openalex.org/W3137092977","doi":"https://doi.org/10.1080/00029890.2021.1867464","title":"An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials","display_name":"An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials","publication_year":2021,"publication_date":"2021-03-23","ids":{"openalex":"https://openalex.org/W3137092977","doi":"https://doi.org/10.1080/00029890.2021.1867464","mag":"3137092977"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2021.1867464","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2021.1867464","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/A5078616413","display_name":"J. Boulanger","orcid":"https://orcid.org/0000-0001-6162-8510"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210163673","display_name":"Laboratoire Ami\u00e9nois de Math\u00e9matique Fondamentale et Appliqu\u00e9e","ror":"https://ror.org/04smxbm79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210163673","https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jacques Boulanger","raw_affiliation_strings":["Department of Mathematics, LAMFA CNRS UMR 7352, 33 Rue Saint-Leu, 80039 Amiens, France"],"raw_orcid":"https://orcid.org/0000-0001-6162-8510","affiliations":[{"raw_affiliation_string":"Department of Mathematics, LAMFA CNRS UMR 7352, 33 Rue Saint-Leu, 80039 Amiens, France","institution_ids":["https://openalex.org/I4210163673","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002442150","display_name":"Jean-Luc Chabert","orcid":"https://orcid.org/0000-0001-6324-043X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210163673","display_name":"Laboratoire Ami\u00e9nois de Math\u00e9matique Fondamentale et Appliqu\u00e9e","ror":"https://ror.org/04smxbm79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210163673","https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Luc Chabert","raw_affiliation_strings":["Department of Mathematics, LAMFA CNRS UMR 7352, 33 Rue Saint-Leu, 80039 Amiens, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, LAMFA CNRS UMR 7352, 33 Rue Saint-Leu, 80039 Amiens, France","institution_ids":["https://openalex.org/I4210163673","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002442150"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210163673"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13412189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"128","issue":"4","first_page":"360","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9682000279426575,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9312000274658203,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8181999325752258},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7926715016365051},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.7292118072509766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7209474444389343},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.655900776386261},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.604697585105896},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5848492383956909},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5638339519500732},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5175230503082275},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.47763577103614807},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3919878900051117},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37954390048980713},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33295273780822754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13943004608154297},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.0609470009803772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04921931028366089}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8181999325752258},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7926715016365051},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.7292118072509766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7209474444389343},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.655900776386261},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.604697585105896},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5848492383956909},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5638339519500732},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5175230503082275},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.47763577103614807},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3919878900051117},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37954390048980713},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33295273780822754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13943004608154297},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0609470009803772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04921931028366089},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2021.1867464","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2021.1867464","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03621210v1","is_oa":false,"landing_page_url":"https://u-picardie.hal.science/hal-03621210","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The American Mathematical Monthly, 2021, 128 (4), pp.360-366. ⟨10.1080/00029890.2021.1867464⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W568384724","https://openalex.org/W1551345846","https://openalex.org/W1979277780","https://openalex.org/W1995459905","https://openalex.org/W2026862908","https://openalex.org/W2323309125","https://openalex.org/W2344593929","https://openalex.org/W2573623072"],"related_works":["https://openalex.org/W2959217929","https://openalex.org/W2954167023","https://openalex.org/W4242866892","https://openalex.org/W2064351239","https://openalex.org/W2949665548","https://openalex.org/W2114983089","https://openalex.org/W42551271","https://openalex.org/W2950188642","https://openalex.org/W2028676759","https://openalex.org/W84644661"],"abstract_inverted_index":{"The":[0],"ring":[1],"Int(Z)":[2,67,76],"of":[3,27,46,57,66,73],"integer-valued":[4],"polynomials":[5],"has":[6],"the":[7,24,50,62],"two-generator":[8],"property,":[9],"which":[10],"means":[11,45],"that":[12],"every":[13],"finitely":[14,63],"generated":[15,19,64],"ideal":[16],"may":[17],"be":[18],"by":[20,44,70],"two":[21,58],"elements.":[22],"As":[23],"known":[25],"proofs":[26,56],"this":[28],"fact":[29],"are":[30,68],"rather":[31],"complicated":[32],"using":[33],"strong":[34],"topological":[35],"arguments,":[36],"we":[37,52],"propose":[38],"here":[39],"a":[40,78],"constructive":[41,55],"proof":[42],"obtained":[43],"elementary":[47],"tools.":[48],"Along":[49],"way,":[51],"also":[53],"obtain":[54],"other":[59],"well-known":[60],"facts:":[61],"ideals":[65,72],"characterized":[69],"their":[71],"values":[74],"and":[75],"is":[77],"two-dimensional":[79],"Pr\u00fcfer":[80],"domain.":[81]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}