{"id":"https://openalex.org/W4412481117","doi":"https://doi.org/10.3390/axioms14070536","title":"On Subprojectivity of Goldie Torsion Modules","display_name":"On Subprojectivity of Goldie Torsion Modules","publication_year":2025,"publication_date":"2025-07-16","ids":{"openalex":"https://openalex.org/W4412481117","doi":"https://doi.org/10.3390/axioms14070536"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070536","pdf_url":"https://www.mdpi.com/2075-1680/14/7/536/pdf?version=1752735043","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/7/536/pdf?version=1752735043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061256797","display_name":"Hashem Bordbar","orcid":"https://orcid.org/0000-0003-3871-217X"},"institutions":[{"id":"https://openalex.org/I192455894","display_name":"University of Nova Gorica","ror":"https://ror.org/00mw0tw28","country_code":"SI","type":"education","lineage":["https://openalex.org/I192455894"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Hashem Bordbar","raw_affiliation_strings":["Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"],"affiliations":[{"raw_affiliation_string":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia","institution_ids":["https://openalex.org/I192455894"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019900168","display_name":"Y\u0131lmaz Dur\u011fun","orcid":"https://orcid.org/0000-0002-1230-8964"},"institutions":[{"id":"https://openalex.org/I55931168","display_name":"Cukurova University","ror":"https://ror.org/05wxkj555","country_code":"TR","type":"education","lineage":["https://openalex.org/I55931168"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Y\u0131lmaz Dur\u011fun","raw_affiliation_strings":["Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye","institution_ids":["https://openalex.org/I55931168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5119008209","display_name":"Yara \u015eihkayad","orcid":null},"institutions":[{"id":"https://openalex.org/I55931168","display_name":"Cukurova University","ror":"https://ror.org/05wxkj555","country_code":"TR","type":"education","lineage":["https://openalex.org/I55931168"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Yara \u015eihkayad","raw_affiliation_strings":["Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, \u00c7ukurova University, Adana 01330, T\u00fcrkiye","institution_ids":["https://openalex.org/I55931168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082670019","display_name":"Erg\u00fcl T\u00fcrkmen","orcid":"https://orcid.org/0000-0002-7082-1176"},"institutions":[{"id":"https://openalex.org/I70387731","display_name":"Amasya \u00dcniversitesi","ror":"https://ror.org/00sbx0y13","country_code":"TR","type":"education","lineage":["https://openalex.org/I70387731"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erg\u00fcl T\u00fcrkmen","raw_affiliation_strings":["Department of Mathematics, Amasya University, Amasya 05100, T\u00fcrkiye"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amasya University, Amasya 05100, T\u00fcrkiye","institution_ids":["https://openalex.org/I70387731"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061256797"],"corresponding_institution_ids":["https://openalex.org/I192455894"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23839325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"536","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9851999878883362,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9724000096321106,"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/invertible-matrix","display_name":"Invertible matrix","score":0.8615763783454895},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.8571898937225342},{"id":"https://openalex.org/keywords/epic","display_name":"EPIC","score":0.6575809121131897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5456023216247559},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5178773403167725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3807576298713684},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0524786114692688}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8615763783454895},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.8571898937225342},{"id":"https://openalex.org/C115519274","wikidata":"https://www.wikidata.org/wiki/Q267903","display_name":"EPIC","level":2,"score":0.6575809121131897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5456023216247559},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5178773403167725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3807576298713684},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0524786114692688},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C90856448","wikidata":"https://www.wikidata.org/wiki/Q431","display_name":"Zoology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14070536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070536","pdf_url":"https://www.mdpi.com/2075-1680/14/7/536/pdf?version=1752735043","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:repozitorij.ung.si:IzpisGradiva.php?id=10213","is_oa":true,"landing_page_url":"https://repozitorij.ung.si/Dokument.php?id=32767&dn=","pdf_url":"https://repozitorij.ung.si/Dokument.php?id=32765&dn=","source":{"id":"https://openalex.org/S7407055115","display_name":"RUNG","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 2075-1680","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:245811d1aec843f5bab8020dafb87b2e","is_oa":true,"landing_page_url":"https://doaj.org/article/245811d1aec843f5bab8020dafb87b2e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 7, p 536 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070536","pdf_url":"https://www.mdpi.com/2075-1680/14/7/536/pdf?version=1752735043","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5074522936","display_name":null,"funder_award_id":"122F130","funder_id":"https://openalex.org/F4320322626","funder_display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu"}],"funders":[{"id":"https://openalex.org/F4320322626","display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu","ror":"https://ror.org/04w9kkr77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412481117.pdf","grobid_xml":"https://content.openalex.org/works/W4412481117.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1542689491","https://openalex.org/W1556497189","https://openalex.org/W1973492157","https://openalex.org/W1985525117","https://openalex.org/W2019547631","https://openalex.org/W2032574897","https://openalex.org/W2098426524","https://openalex.org/W2149669101","https://openalex.org/W2164139224","https://openalex.org/W2929195203","https://openalex.org/W3030820427","https://openalex.org/W3035071593","https://openalex.org/W3104762721","https://openalex.org/W3138615358","https://openalex.org/W3174679721","https://openalex.org/W4252544066","https://openalex.org/W4292101331","https://openalex.org/W4300662053","https://openalex.org/W4324347818","https://openalex.org/W4388302355","https://openalex.org/W4390664807","https://openalex.org/W4392868904","https://openalex.org/W4399427370","https://openalex.org/W4400164102","https://openalex.org/W6643504013"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2151979312","https://openalex.org/W1480231236","https://openalex.org/W1488337530","https://openalex.org/W2169393985","https://openalex.org/W2606632758","https://openalex.org/W4251428025","https://openalex.org/W3094193311","https://openalex.org/W4200333915","https://openalex.org/W4300961093"],"abstract_inverted_index":{"Recently,":[0],"the":[1,16,31,57],"concept":[2],"of":[3,14,18,34,60],"subprojectivity":[4,32,58],"domains":[5],"for":[6],"modules":[7],"has":[8],"been":[9],"introduced":[10],"as":[11,46,50],"a":[12,22,43,74,78],"means":[13],"quantifying":[15],"level":[17],"projectivity":[19],"exhibited":[20],"by":[21],"module.":[23],"In":[24,38,69],"this":[25],"research":[26],"article,":[27],"we":[28,40,71],"focus":[29],"on":[30],"domain":[33,59],"Goldie":[35,62,99],"torsion":[36,63,100],"modules.":[37],"particular,":[39],"establish":[41],"that":[42,73],"ring":[44,81],"denoted":[45],"R":[47],"is":[48,65,77,94],"classified":[49],"right":[51,75,79],"nonsingular":[52,80],"if":[53,56,82,85],"and":[54,83],"only":[55,84],"each":[61,98],"module":[64,87,101],"closed":[66],"under":[67],"submodules.":[68],"addition,":[70],"demonstrate":[72],"C-ring":[76],"every":[86],"possesses":[88],"an":[89,103],"epic":[90,104],"ecf-flat":[91],"envelope,":[92],"which":[93],"further":[95],"equivalent":[96],"to":[97],"having":[102],"projective":[105],"envelope.":[106]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}