{"id":"https://openalex.org/W2036950288","doi":"https://doi.org/10.1142/s0218196712500361","title":"IS AN IRNG SINGLY GENERATED AS AN IDEAL?","display_name":"IS AN IRNG SINGLY GENERATED AS AN IDEAL?","publication_year":2012,"publication_date":"2012-02-13","ids":{"openalex":"https://openalex.org/W2036950288","doi":"https://doi.org/10.1142/s0218196712500361","mag":"2036950288"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500361","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500361","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1112.1802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"NICOLAS MONOD","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"NICOLAS MONOD","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":null,"display_name":"NARUTAKA OZAWA","orcid":null},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"NARUTAKA OZAWA","raw_affiliation_strings":["Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":null,"display_name":"ANDREAS THOM","orcid":null},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"ANDREAS THOM","raw_affiliation_strings":["Universit\u00e4t Leipzig, PF 100920, 04009 Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Leipzig, PF 100920, 04009 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13144218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"04","first_page":"1250036","last_page":"1250036"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.5328999757766724,"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":0.5328999757766724,"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/T10849","display_name":"Finite Group Theory Research","score":0.20829999446868896,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.060499999672174454,"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/idempotence","display_name":"Idempotence","score":0.8260999917984009},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.6836000084877014},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6367999911308289},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5989999771118164},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.49219998717308044},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34529998898506165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8914999961853027},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.8260999917984009},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.6836000084877014},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6367999911308289},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5989999771118164},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.49219998717308044},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46070000529289246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34850001335144043},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.30730000138282776},{"id":"https://openalex.org/C58249144","wikidata":"https://www.wikidata.org/wiki/Q7597316","display_name":"Stallings theorem about ends of groups","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2662000060081482}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196712500361","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500361","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:arXiv.org:1112.1802","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.1802","pdf_url":"https://arxiv.org/pdf/1112.1802","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:170552","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/170552","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1112.1802","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.1802","pdf_url":"https://arxiv.org/pdf/1112.1802","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2065772166","https://openalex.org/W2156896240"],"related_works":[],"abstract_inverted_index":{"Recall":[0],"that":[1,34,46],"a":[2,5,40,53,62],"rng":[3,23,55],"is":[4,8,25,32,36,48,74],"ring":[6],"which":[7],"possibly":[9],"non-unital.":[10],"In":[11],"this":[12],"note,":[13],"we":[14],"address":[15],"the":[16,37,50,68],"problem":[17,70],"whether":[18],"every":[19],"finitely":[20,57],"generated":[21,27],"idempotent":[22],"(irng)":[24],"singly":[26],"as":[28],"an":[29],"ideal.":[30],"It":[31],"well-known":[33],"it":[35,47],"case":[38,51],"for":[39,52,61,71],"commutative":[41],"irng.":[42,64],"We":[43],"prove":[44],"here":[45],"also":[49],"free":[54],"on":[56],"many":[58],"idempotents":[59],"and":[60],"finite":[63],"A":[65],"relation":[66],"to":[67],"Wiegold":[69],"perfect":[72],"groups":[73],"discussed.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
