{"id":"https://openalex.org/W2796787033","doi":"https://doi.org/10.1080/00029890.2018.1436841","title":"An Irreducibility Criterion for Polynomials with Integer Coefficients","display_name":"An Irreducibility Criterion for Polynomials with Integer Coefficients","publication_year":2018,"publication_date":"2018-04-12","ids":{"openalex":"https://openalex.org/W2796787033","doi":"https://doi.org/10.1080/00029890.2018.1436841","mag":"2796787033"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1436841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1436841","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/A5043779349","display_name":"Anuj Jakhar","orcid":"https://orcid.org/0009-0007-5951-2261"},"institutions":[{"id":"https://openalex.org/I165916956","display_name":"Indian Institute of Science Education and Research Mohali","ror":"https://ror.org/01vztzd79","country_code":"IN","type":"education","lineage":["https://openalex.org/I165916956"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Anuj Jakhar","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohali, Knowledge City, Sector - 81, SAS Nagar, Mohali, Punjab 140306, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohali, Knowledge City, Sector - 81, SAS Nagar, Mohali, Punjab 140306, India","institution_ids":["https://openalex.org/I165916956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043779349"],"corresponding_institution_ids":["https://openalex.org/I165916956"],"apc_list":null,"apc_paid":null,"fwci":0.3431,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50413184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"125","issue":"5","first_page":"464","last_page":"465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9873999953269958,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9690999984741211,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/irreducibility","display_name":"Irreducibility","score":0.9355744123458862},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.8423526883125305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7878280878067017},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6014243960380554},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5116108059883118},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.47496625781059265},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.47025004029273987},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.4504117965698242},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.44631773233413696},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4433283507823944},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40600496530532837},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34599989652633667},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.2629808187484741},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11715766787528992},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0566694438457489},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.0547347366809845}],"concepts":[{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.9355744123458862},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.8423526883125305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7878280878067017},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6014243960380554},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5116108059883118},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.47496625781059265},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.47025004029273987},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.4504117965698242},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.44631773233413696},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4433283507823944},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40600496530532837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34599989652633667},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2629808187484741},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11715766787528992},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0566694438457489},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0547347366809845},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1436841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1436841","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2259613383","https://openalex.org/W2528178140"],"related_works":["https://openalex.org/W2012860697","https://openalex.org/W4286909400","https://openalex.org/W3125460591","https://openalex.org/W2081607056","https://openalex.org/W2070537393","https://openalex.org/W3147630167","https://openalex.org/W1985839497","https://openalex.org/W3148568540","https://openalex.org/W2168893271","https://openalex.org/W2796787033"],"abstract_inverted_index":{"We":[0],"provide":[1],"irreducibility":[2],"conditions":[3],"for":[4],"polynomials":[5,34],"f(x)":[6],"with":[7,10],"integer":[8],"coefficients,":[9],"f":[11],"written":[12],"in":[13],"\u03c6(x)-expansion,":[14],"where":[15],"\u03c6":[16],"is":[17],"monic":[18],"and":[19],"irreducible":[20,33],"modulo":[21],"some":[22,28],"prime":[23],"number":[24],"p.":[25],"Examples":[26],"of":[27,31],"explicit":[29],"families":[30],"such":[32],"are":[35],"also":[36],"given.":[37]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}