{"id":"https://openalex.org/W7215998403","doi":"https://doi.org/10.48550/arxiv.2610.00116","title":"A Reduced Non-McCoy Ring with the Annihilator Condition and $(A_2)$","display_name":"A Reduced Non-McCoy Ring with the Annihilator Condition and $(A_2)$","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7215998403","doi":"https://doi.org/10.48550/arxiv.2610.00116"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00116","pdf_url":"https://arxiv.org/pdf/2610.00116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.00116","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111236249","display_name":"Viet-Hoang Tran","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran, Viet-Hoang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5155623010","display_name":"Tan M. Nguyen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Tan M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/T11673","display_name":"Advanced Topics in Algebra","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reduced-rings","display_name":"reduced rings","score":0.8489999771118164},{"id":"https://openalex.org/keywords/annihilator-conditions","display_name":"annihilator conditions","score":0.9909999966621399},{"id":"https://openalex.org/keywords/ring-theory","display_name":"ring theory","score":0.503000020980835},{"id":"https://openalex.org/keywords/countable-rings","display_name":"countable rings","score":0.6570000052452087}],"concepts":[{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.9528999924659729},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.7908999919891357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6468999981880188},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5281999707221985},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4668999910354614},{"id":"https://openalex.org/C100044566","wikidata":"https://www.wikidata.org/wiki/Q6423024","display_name":"Reduced ring","level":5,"score":0.44690001010894775},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C156923205","wikidata":"https://www.wikidata.org/wiki/Q2905043","display_name":"Principal ideal ring","level":4,"score":0.36500000953674316},{"id":"https://openalex.org/C202836834","wikidata":"https://www.wikidata.org/wiki/Q2895708","display_name":"Primitive ring","level":5,"score":0.337799996137619},{"id":"https://openalex.org/C128134353","wikidata":"https://www.wikidata.org/wiki/Q2634401","display_name":"Boolean ring","level":5,"score":0.3296999931335449},{"id":"https://openalex.org/C88619972","wikidata":"https://www.wikidata.org/wiki/Q7280488","display_name":"Radical of a ring","level":5,"score":0.3278000056743622},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32339999079704285},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25609999895095825},{"id":"https://openalex.org/C83920498","wikidata":"https://www.wikidata.org/wiki/Q2326800","display_name":"Simple ring","level":5,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00116","pdf_url":"https://arxiv.org/pdf/2610.00116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.00116","doi":"https://doi.org/10.48550/arxiv.2610.00116","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00116","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.00116","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00116","pdf_url":"https://arxiv.org/pdf/2610.00116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215998403.pdf","grobid_xml":"https://content.openalex.org/works/W7215998403.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2954377069","https://openalex.org/W2039998466","https://openalex.org/W2155439619","https://openalex.org/W2290196380","https://openalex.org/W2270880389","https://openalex.org/W2080355451","https://openalex.org/W3031960548","https://openalex.org/W2103436807","https://openalex.org/W2905578392","https://openalex.org/W2724843782"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"asked":[3],"whether":[4],"a":[5,36,49],"reduced":[6],"non-McCoy":[7],"ring":[8,50],"can":[9],"satisfy":[10],"both":[11],"the":[12,42],"annihilator":[13,43],"condition":[14,44],"and":[15,39],"$(A_n)$":[16],"for":[17],"some":[18],"$n":[19],"\\geq":[20],"2$.":[21],"In":[22],"this":[23],"work,":[24],"we":[25],"prove":[26],"that":[27,41],"such":[28],"rings":[29],"exist":[30],"exactly":[31],"when":[32],"$n=2$,":[33],"by":[34],"constructing":[35],"countable":[37],"example":[38],"showing":[40],"together":[45],"with":[46],"$(A_3)$":[47],"forces":[48],"to":[51],"be":[52],"McCoy.":[53]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-03T00:00:00"}
