{"id":"https://openalex.org/W4399027632","doi":"https://doi.org/10.30598/barekengvol18iss2pp1307-1316","title":"THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P)","display_name":"THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P)","publication_year":2024,"publication_date":"2024-05-25","ids":{"openalex":"https://openalex.org/W4399027632","doi":"https://doi.org/10.30598/barekengvol18iss2pp1307-1316"},"language":"en","primary_location":{"id":"doi:10.30598/barekengvol18iss2pp1307-1316","doi":"https://doi.org/10.30598/barekengvol18iss2pp1307-1316","is_oa":true,"landing_page_url":"http://dx.doi.org/10.30598/barekengvol18iss2pp1307-1316","pdf_url":null,"source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://dx.doi.org/10.30598/barekengvol18iss2pp1307-1316","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098839993","display_name":"Shinta Nur Alfiana","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Shinta Nur Alfiana","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia","institution_ids":["https://openalex.org/I11855966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054935769","display_name":"Nikken Prima Puspita","orcid":"https://orcid.org/0000-0002-0127-2628","observed_orcids":["https://orcid.org/0000-0002-0127-2628"]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Nikken Prima Puspita","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia","institution_ids":["https://openalex.org/I11855966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040807353","display_name":"Widowati Widowati","orcid":"https://orcid.org/0000-0002-4372-6501","observed_orcids":["https://orcid.org/0000-0002-4372-6501","https://orcid.org/0009-0007-7978-9591"]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Widowati Widowati","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro, Indonesia","institution_ids":["https://openalex.org/I11855966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11855966"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"2","first_page":"1307","last_page":"1316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":1.0,"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":1.0,"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":0.0,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"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/clean-rings","display_name":"clean rings","score":0.9490000009536743},{"id":"https://openalex.org/keywords/subrings","display_name":"subrings","score":0.7160000205039978},{"id":"https://openalex.org/keywords/matrix-rings","display_name":"matrix rings","score":0.7039999961853027},{"id":"https://openalex.org/keywords/idempotents","display_name":"idempotents","score":0.8270000219345093},{"id":"https://openalex.org/keywords/units","display_name":"units","score":0.7310000061988831},{"id":"https://openalex.org/keywords/regular-elements","display_name":"regular elements","score":0.9259999990463257},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.4490000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4060342013835907}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.30598/barekengvol18iss2pp1307-1316","doi":"https://doi.org/10.30598/barekengvol18iss2pp1307-1316","is_oa":true,"landing_page_url":"http://dx.doi.org/10.30598/barekengvol18iss2pp1307-1316","pdf_url":null,"source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3a866f82c5fd443f8fdfcaccbea63727","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/3a866f82c5fd443f8fdfcaccbea63727","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Barekeng, Vol 18, Iss 2, Pp 1307-1316 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.30598/barekengvol18iss2pp1307-1316","doi":"https://doi.org/10.30598/barekengvol18iss2pp1307-1316","is_oa":true,"landing_page_url":"http://dx.doi.org/10.30598/barekengvol18iss2pp1307-1316","pdf_url":null,"source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1516603806","https://openalex.org/W2012820152","https://openalex.org/W2095197235","https://openalex.org/W2099916937","https://openalex.org/W2249377867","https://openalex.org/W2897437778"],"related_works":["https://openalex.org/W1659030969","https://openalex.org/W2010924616","https://openalex.org/W2561771621","https://openalex.org/W2057646624","https://openalex.org/W2246807294","https://openalex.org/W4297877480","https://openalex.org/W2035865511","https://openalex.org/W2272799936","https://openalex.org/W2963550218","https://openalex.org/W7052721933"],"abstract_inverted_index":{"Let":[0],"be":[1,8,18,54,87],"a":[2,9,24,39,42,60,78,93,115,167],"ring.":[3,44],"Ring":[4],"is":[5,38,77,107,114,166],"said":[6],"to":[7,150],"clean":[10,43],"ring":[11,37,76,79,85,116,123,168],"if":[12],"every":[13,81],"element":[14,62,82],"of":[15,23,41,50,59,83,92,102,117,120,139,142,146,154,157,160,169],"R":[16],"can":[17,53,86],"expressed":[19,88],"as":[20,56,89],"the":[21,57,84,90,100,110,118,133,140,152,158],"sum":[22,58,91],"unit":[25],"and":[26,63,95,99,105],"an":[27,46,64,96],"idempotent":[28,65,97,106],"element.":[29,66],"Furthermore,":[30],"there":[31,113],"are":[32,149],"r-clean":[33,36,47,69,75,138,156],"rings.":[34],"An":[35],"generalization":[40],"In":[45,127],"ring,":[48],"all":[49],"its":[51],"elements":[52],"represented":[55],"regular":[61,94,104],"Moreover,":[67],"strongly":[68,74,137,155],"rings":[70],"were":[71],"introduced.":[72],"A":[73],"where":[80],"element,":[98],"multiplication":[101],"that":[103,165],"commutative.":[108],"On":[109],"other":[111],"hand,":[112],"set":[119],"matrices":[121],"over":[122,171],"denotes":[124],"by":[125],".":[126,143,161,172],"this":[128,147],"paper,":[129],"we":[130,163],"will":[131],"discuss":[132],"cleanness":[134],"properties,":[135],"especially":[136],"subring":[141,159],"The":[144],"aims":[145],"paper":[148],"find":[151],"characteristics":[153],"Here,":[162],"assumed":[164],"matrix":[170]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2024-05-26T00:00:00"}