{"id":"https://openalex.org/W1550022756","doi":"https://doi.org/10.1090/s0025-5718-2010-02383-x","title":"Fundamentality of a cubic unit $u$ for $\\mathbb {Z}[u]$","display_name":"Fundamentality of a cubic unit $u$ for $\\mathbb {Z}[u]$","publication_year":2010,"publication_date":"2010-07-29","ids":{"openalex":"https://openalex.org/W1550022756","doi":"https://doi.org/10.1090/s0025-5718-2010-02383-x","mag":"1550022756"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2010-02383-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02383-x","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02383-X/S0025-5718-2010-02383-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02383-X/S0025-5718-2010-02383-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009189495","display_name":"J. Beers","orcid":null},"institutions":[{"id":"https://openalex.org/I64281891","display_name":"College of New Jersey","ror":"https://ror.org/02nx5r318","country_code":"US","type":"education","lineage":["https://openalex.org/I64281891"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Beers","raw_affiliation_strings":["The College of New Jersey, Ewing, New Jersey 08628"],"affiliations":[{"raw_affiliation_string":"The College of New Jersey, Ewing, New Jersey 08628","institution_ids":["https://openalex.org/I64281891"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025948517","display_name":"D. Henshaw","orcid":null},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Henshaw","raw_affiliation_strings":["Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052831183","display_name":"C. McCall","orcid":null},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. K. McCall","raw_affiliation_strings":["Department of Mathematics, 719 Patterson Office Tower, University of Kentucky, Lexington, Kentucky 40506-0027"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, 719 Patterson Office Tower, University of Kentucky, Lexington, Kentucky 40506-0027","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008416132","display_name":"S. B. Mulay","orcid":"https://orcid.org/0000-0002-6712-6260"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. B. Mulay","raw_affiliation_strings":["Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300","Department of Mathematics, University of Tennessee, Knoxville, Tennessee, 37996-1300"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, Tennessee, 37996-1300","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034549091","display_name":"Mark Spindler","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Spindler","raw_affiliation_strings":["Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5009189495"],"corresponding_institution_ids":["https://openalex.org/I64281891"],"apc_list":null,"apc_paid":null,"fwci":0.3793,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54693062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"80","issue":"273","first_page":"563","last_page":"578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"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":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.84320068359375},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.7443896532058716},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.548957347869873},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5004515647888184},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4726502001285553},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37652596831321716},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07078126072883606},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.04014021158218384},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.03445693850517273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.84320068359375},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.7443896532058716},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.548957347869873},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5004515647888184},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4726502001285553},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37652596831321716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07078126072883606},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.04014021158218384},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.03445693850517273},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2010-02383-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02383-x","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02383-X/S0025-5718-2010-02383-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2010-02383-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02383-x","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02383-X/S0025-5718-2010-02383-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3708095926","display_name":"REU Site in Mathematics at The University of Tennessee","funder_award_id":"0552774","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1550022756.pdf","grobid_xml":"https://content.openalex.org/works/W1550022756.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W186937753","https://openalex.org/W1496801598","https://openalex.org/W1966361499","https://openalex.org/W1972228998","https://openalex.org/W2050068482","https://openalex.org/W2062788415"],"related_works":["https://openalex.org/W4241330371","https://openalex.org/W611386996","https://openalex.org/W4389363760","https://openalex.org/W3203470546","https://openalex.org/W1988723200","https://openalex.org/W3038086597","https://openalex.org/W2980963558","https://openalex.org/W2371343292","https://openalex.org/W4287208209","https://openalex.org/W1997795239"],"abstract_inverted_index":{"Consider":[0],"a":[1,10,19,36],"cubic":[2],"unit":[3,21],"$u$":[4,17],"of":[5,13,22],"positive":[6],"discriminant.":[7],"We":[8],"present":[9],"computational":[11],"proof":[12],"the":[14,23,32],"fact":[15],"that":[16],"is":[18],"fundamental":[20],"order":[24],"$\\mathbb":[25],"{Z}[u]$":[26],"in":[27],"most":[28],"cases":[29],"and":[30],"determine":[31],"exceptions.":[33],"This":[34],"extends":[35],"similar":[37],"(but":[38],"restrictive)":[39],"result":[40],"due":[41],"to":[42],"E.":[43],"Thomas.":[44]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}