{"id":"https://openalex.org/W3003204758","doi":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","title":"Some Results on C-retractable Modules","display_name":"Some Results on C-retractable Modules","publication_year":2020,"publication_date":"2020-01-31","ids":{"openalex":"https://openalex.org/W3003204758","doi":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","mag":"3003204758"},"language":"en","primary_location":{"id":"doi:10.29020/nybg.ejpam.v13i1.3588","doi":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","is_oa":true,"landing_page_url":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","pdf_url":"https://www.ejpam.com/index.php/ejpam/article/download/3588/859","source":{"id":"https://openalex.org/S2764475867","display_name":"European Journal of Pure and Applied Mathematics","issn_l":"1307-5543","issn":["1307-5543"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Pure and Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.ejpam.com/index.php/ejpam/article/download/3588/859","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019489858","display_name":"Abdoul Djibril Diallo","orcid":"https://orcid.org/0000-0002-1791-0639","observed_orcids":["https://orcid.org/0000-0002-1791-0639"]},"institutions":[{"id":"https://openalex.org/I96840727","display_name":"Cheikh Anta Diop University","ror":"https://ror.org/04je6yw13","country_code":"SN","type":"education","lineage":["https://openalex.org/I96840727"]}],"countries":["SN"],"is_corresponding":true,"raw_author_name":"Abdoul Djibril Diallo","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences et Techniques, Universit\u00e9 Cheikh Anta Diop, Dakar, S\u00e9n\u00e9gal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences et Techniques, Universit\u00e9 Cheikh Anta Diop, Dakar, S\u00e9n\u00e9gal","institution_ids":["https://openalex.org/I96840727"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025927627","display_name":"Papa Cheikhou Diop","orcid":"https://orcid.org/0000-0003-0628-0018","observed_orcids":["https://orcid.org/0000-0003-0628-0018"]},"institutions":[{"id":"https://openalex.org/I79793008","display_name":"Universit\u00e9 de Thi\u00e8s","ror":"https://ror.org/05nfkgg69","country_code":"SN","type":"education","lineage":["https://openalex.org/I79793008"]}],"countries":["SN"],"is_corresponding":false,"raw_author_name":"Papa Cheikhou Diop","raw_affiliation_strings":["Thi\u00e8s University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thi\u00e8s University","institution_ids":["https://openalex.org/I79793008"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mamadou Barry","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I96840727","display_name":"Cheikh Anta Diop University","ror":"https://ror.org/04je6yw13","country_code":"SN","type":"education","lineage":["https://openalex.org/I96840727"]}],"countries":["SN"],"is_corresponding":false,"raw_author_name":"Mamadou Barry","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences et Techniques, Universit\u00e9 Cheikh Anta Diop, Dakar, S\u00e9n\u00e9gal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et Informatique, Facult\u00e9 des Sciences et Techniques, Universit\u00e9 Cheikh Anta Diop, Dakar, S\u00e9n\u00e9gal","institution_ids":["https://openalex.org/I96840727"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019489858"],"corresponding_institution_ids":["https://openalex.org/I96840727"],"apc_list":null,"apc_paid":null,"fwci":0.429,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46468099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"13","issue":"1","first_page":"158","last_page":"169"},"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/T10287","display_name":"Algebraic structures and combinatorial models","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"}},{"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projective-modules","display_name":"projective modules","score":0.8539999723434448},{"id":"https://openalex.org/keywords/nonsingular-modules","display_name":"nonsingular modules","score":0.7910000085830688},{"id":"https://openalex.org/keywords/uniform-modules","display_name":"uniform modules","score":0.765999972820282},{"id":"https://openalex.org/keywords/quasi-injective-modules","display_name":"quasi-injective modules","score":0.6890000104904175},{"id":"https://openalex.org/keywords/extending-modules","display_name":"extending modules","score":0.75}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375579118728638},{"id":"https://openalex.org/C99463465","wikidata":"https://www.wikidata.org/wiki/Q2716519","display_name":"Injective module","level":3,"score":0.8283135294914246},{"id":"https://openalex.org/C35729967","wikidata":"https://www.wikidata.org/wiki/Q18848","display_name":"Module","level":4,"score":0.7664645910263062},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.611088752746582},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5885549783706665},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5717418193817139},{"id":"https://openalex.org/C130430149","wikidata":"https://www.wikidata.org/wiki/Q1292333","display_name":"Free module","level":3,"score":0.5409269332885742},{"id":"https://openalex.org/C32268108","wikidata":"https://www.wikidata.org/wiki/Q942423","display_name":"Projective module","level":3,"score":0.5139162540435791},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.5004861354827881},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4752980172634125},{"id":"https://openalex.org/C31937215","wikidata":"https://www.wikidata.org/wiki/Q956233","display_name":"Simple module","level":3,"score":0.4707682132720947},{"id":"https://openalex.org/C2778153370","wikidata":"https://www.wikidata.org/wiki/Q2896709","display_name":"Endomorphism ring","level":3,"score":0.46857547760009766},{"id":"https://openalex.org/C148896618","wikidata":"https://www.wikidata.org/wiki/Q1426191","display_name":"Flat module","level":4,"score":0.44209614396095276},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.44057926535606384},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.432912141084671},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.41590166091918945},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3283872604370117},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.32607632875442505},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.24365335702896118},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.2360820472240448},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.29020/nybg.ejpam.v13i1.3588","doi":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","is_oa":true,"landing_page_url":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","pdf_url":"https://www.ejpam.com/index.php/ejpam/article/download/3588/859","source":{"id":"https://openalex.org/S2764475867","display_name":"European Journal of Pure and Applied Mathematics","issn_l":"1307-5543","issn":["1307-5543"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Pure and Applied Mathematics","raw_type":"journal-article"},{"id":"doi:10.29020/nybg.ejpam.v1i1.3588","doi":"https://doi.org/10.29020/nybg.ejpam.v1i1.3588","is_oa":true,"landing_page_url":"https://doi.org/10.29020/nybg.ejpam.v1i1.3588","pdf_url":null,"source":{"id":"https://openalex.org/S2764475867","display_name":"European Journal of Pure and Applied Mathematics","issn_l":"1307-5543","issn":["1307-5543"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Pure and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.29020/nybg.ejpam.v13i1.3588","doi":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","is_oa":true,"landing_page_url":"https://doi.org/10.29020/nybg.ejpam.v13i1.3588","pdf_url":"https://www.ejpam.com/index.php/ejpam/article/download/3588/859","source":{"id":"https://openalex.org/S2764475867","display_name":"European Journal of Pure and Applied Mathematics","issn_l":"1307-5543","issn":["1307-5543"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Pure and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3003204758.pdf","grobid_xml":"https://content.openalex.org/works/W3003204758.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W91180184","https://openalex.org/W1497483297","https://openalex.org/W1507519150","https://openalex.org/W1946249162","https://openalex.org/W2031102356","https://openalex.org/W2033919458","https://openalex.org/W2081109572","https://openalex.org/W2088696921","https://openalex.org/W2162655953","https://openalex.org/W2169104917","https://openalex.org/W2746331786","https://openalex.org/W4206738103"],"related_works":["https://openalex.org/W2963125632","https://openalex.org/W2145755159","https://openalex.org/W3193452147","https://openalex.org/W2047484498","https://openalex.org/W4309008683","https://openalex.org/W2554712836","https://openalex.org/W4205956050","https://openalex.org/W4387914758","https://openalex.org/W4281872577","https://openalex.org/W4224044579"],"abstract_inverted_index":{"An":[0],"R-module":[1],"M":[2,13],"is":[3,34,44,51,63,87,95,103,118],"called":[4],"c-retractable":[5,49,85,101,117],"if":[6],"there":[7],"exists":[8],"a":[9,41,52,56,60,64,84,98,106,119],"nonzero":[10,18],"homomorphism":[11],"from":[12],"to":[14,105],"any":[15],"of":[16,29,55,67,109],"its":[17],"complement":[19],"submodules.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24],"provide":[25],"some":[26],"new":[27],"results":[28],"c-":[30],"retractable":[31],"modules.":[32,111],"It":[33],"shown":[35,96],"that":[36,97],"every":[37,116],"projective":[38],"module":[39,50,58,61,86,102],"over":[40,114],"right":[42],"SI-ring":[43],"c-retractable.":[45],"A":[46],"dual":[47],"Baer":[48],"direct":[53,65,107],"sum":[54,66,108],"Z2-torsion":[57],"and":[59,91],"which":[62,115],"nonsingular":[68],"uniform":[69,110],"quasi-Baer":[70],"modules":[71],"whose":[72],"endomorphism":[73],"rings":[74,113],"are":[75,80,121],"semi-":[76],"local":[77],"quasi-Baer.":[78],"Conditions":[79],"found":[81],"under":[82],"which,":[83],"extending,":[88],"quasi-continuous,":[89],"quasi-injective":[90],"retractable.":[92],"Also,":[93],"it":[94],"locally":[99],"noetherian":[100],"homo-related":[104],"Finally,":[112],"C4-module":[120],"determined.":[122]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2020-02-07T00:00:00"}