{"id":"https://openalex.org/W1910698038","doi":"https://doi.org/10.1216/rmj-2016-46-4-1309","title":"$\\tau $-Regular factorization in commutative rings with zero-divisors","display_name":"$\\tau $-Regular factorization in commutative rings with zero-divisors","publication_year":2016,"publication_date":"2016-08-01","ids":{"openalex":"https://openalex.org/W1910698038","doi":"https://doi.org/10.1216/rmj-2016-46-4-1309","mag":"1910698038"},"language":"en","primary_location":{"id":"doi:10.1216/rmj-2016-46-4-1309","doi":"https://doi.org/10.1216/rmj-2016-46-4-1309","is_oa":true,"landing_page_url":"https://doi.org/10.1216/rmj-2016-46-4-1309","pdf_url":"https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-46/issue-4/tau--Regular-factorization-in-commutative-rings-with-zero-divisors/10.1216/RMJ-2016-46-4-1309.pdf","source":{"id":"https://openalex.org/S118967163","display_name":"Rocky Mountain Journal of Mathematics","issn_l":"0035-7596","issn":["0035-7596","1945-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4320800688","host_organization_name":"Rocky Mountain Mathematics Consortium","host_organization_lineage":["https://openalex.org/P4320800688"],"host_organization_lineage_names":["Rocky Mountain Mathematics Consortium"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rocky Mountain Journal of Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W1910698038"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-46/issue-4/tau--Regular-factorization-in-commutative-rings-with-zero-divisors/10.1216/RMJ-2016-46-4-1309.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005758642","display_name":"Christopher Park Mooney","orcid":"https://orcid.org/0000-0002-6003-4603","observed_orcids":["https://orcid.org/0000-0002-6003-4603"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher Park Mooney","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005758642"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":"46","issue":"4","first_page":"1309","last_page":"1349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0003000000142492354,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":9.999999747378752e-05,"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/factorization-theory","display_name":"factorization theory","score":0.6610000133514404},{"id":"https://openalex.org/keywords/regular-elements","display_name":"regular elements","score":0.7260000109672546},{"id":"https://openalex.org/keywords/irreducible-elements","display_name":"irreducible elements","score":0.8109999895095825},{"id":"https://openalex.org/keywords/associates","display_name":"associates","score":0.7689999938011169}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.902643084526062},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.8400683403015137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7367510795593262},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6842403411865234},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.6732938289642334},{"id":"https://openalex.org/C137559481","wikidata":"https://www.wikidata.org/wiki/Q1231787","display_name":"Dixon's factorization method","level":5,"score":0.5467804670333862},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.5195448994636536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5098592638969421},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4819221794605255},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4254133701324463},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.42441526055336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0991005003452301},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0557914674282074},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1216/rmj-2016-46-4-1309","doi":"https://doi.org/10.1216/rmj-2016-46-4-1309","is_oa":true,"landing_page_url":"https://doi.org/10.1216/rmj-2016-46-4-1309","pdf_url":"https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-46/issue-4/tau--Regular-factorization-in-commutative-rings-with-zero-divisors/10.1216/RMJ-2016-46-4-1309.pdf","source":{"id":"https://openalex.org/S118967163","display_name":"Rocky Mountain Journal of Mathematics","issn_l":"0035-7596","issn":["0035-7596","1945-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4320800688","host_organization_name":"Rocky Mountain Mathematics Consortium","host_organization_lineage":["https://openalex.org/P4320800688"],"host_organization_lineage_names":["Rocky Mountain Mathematics Consortium"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rocky Mountain Journal of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1401.0091","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.0091","pdf_url":"https://arxiv.org/pdf/1401.0091","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":"mag:1910698038","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1401.0091.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CULeuclid:euclid.rmjm/1476884585","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.rmjm/1476884585","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1401.0091","doi":"https://doi.org/10.48550/arxiv.1401.0091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1401.0091","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1216/rmj-2016-46-4-1309","doi":"https://doi.org/10.1216/rmj-2016-46-4-1309","is_oa":true,"landing_page_url":"https://doi.org/10.1216/rmj-2016-46-4-1309","pdf_url":"https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-46/issue-4/tau--Regular-factorization-in-commutative-rings-with-zero-divisors/10.1216/RMJ-2016-46-4-1309.pdf","source":{"id":"https://openalex.org/S118967163","display_name":"Rocky Mountain Journal of Mathematics","issn_l":"0035-7596","issn":["0035-7596","1945-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4320800688","host_organization_name":"Rocky Mountain Mathematics Consortium","host_organization_lineage":["https://openalex.org/P4320800688"],"host_organization_lineage_names":["Rocky Mountain Mathematics Consortium"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rocky Mountain Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1910698038.pdf","grobid_xml":"https://content.openalex.org/works/W1910698038.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W130841307","https://openalex.org/W578591961","https://openalex.org/W1138798142","https://openalex.org/W1415576118","https://openalex.org/W1518525482","https://openalex.org/W1972537709","https://openalex.org/W1976667869","https://openalex.org/W1990434472","https://openalex.org/W1991813034","https://openalex.org/W2010753359","https://openalex.org/W2030520667","https://openalex.org/W2031553948","https://openalex.org/W2048064275","https://openalex.org/W2051749875","https://openalex.org/W2053399991","https://openalex.org/W2055954063","https://openalex.org/W2057064971","https://openalex.org/W2060844765","https://openalex.org/W2068826805","https://openalex.org/W2089217833","https://openalex.org/W2143631753","https://openalex.org/W2152342890","https://openalex.org/W2316437449","https://openalex.org/W2398054713","https://openalex.org/W2486163388","https://openalex.org/W3217001731","https://openalex.org/W4213169272","https://openalex.org/W4242899010","https://openalex.org/W4248537544"],"related_works":["https://openalex.org/W1518525482","https://openalex.org/W4243507005","https://openalex.org/W130841307","https://openalex.org/W4248296976","https://openalex.org/W4248537544","https://openalex.org/W2602650846","https://openalex.org/W3193522735","https://openalex.org/W1967923818"],"abstract_inverted_index":{"Recently":[0],"there":[1],"has":[2],"been":[3],"a":[4],"flurry":[5],"of":[6,42,58,74,84,115],"research":[7],"on":[8,39],"generalized":[9],"factorization":[10,31,70,76,119,128],"techniques":[11],"in":[12,32,123,129],"both":[13],"integral":[14],"domains":[15],"and":[16,48,86],"rings":[17,33,63,130],"with":[18,34,64,131],"zero-divisors,":[19],"namely,":[20],"$\\tau":[21,59],"$-factorization.":[22],"There":[23],"are":[24],"several":[25],"ways":[26],"that":[27,95,121],"authors":[28],"have":[29],"studied":[30],"zero-divisors.":[35,132],"This":[36,110],"paper":[37],"focuses":[38],"the":[40,56,68,81,96,116,124],"method":[41],"regular":[43,69,75,90,106],"factorizations":[44],"introduced":[45],"by":[46,66,100],"Anderson":[47],"Valdes-Leon.":[49],"We":[50,92],"investigate":[51],"how":[52],"one":[53],"can":[54],"extend":[55],"notion":[57],"$-factorization":[60],"to":[61],"commutative":[62],"zero-divisors":[65],"using":[67],"approach.":[71],"The":[72],"study":[73],"is":[77,108],"particularly":[78],"effective":[79],"because":[80],"distinct":[82],"notions":[83],"associate":[85],"irreducible":[87],"coincide":[88],"for":[89],"elements.":[91],"also":[93,102],"note":[94],"popular":[97],"U-factorization":[98],"developed":[99],"Fletcher":[101],"coincides":[103],"since":[104],"every":[105],"divisor":[107],"essential.":[109],"will":[111],"greatly":[112],"simplify":[113],"many":[114],"cumbersome":[117],"finite":[118],"definitions":[120],"exist":[122],"literature":[125],"when":[126],"studying":[127]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
