{"id":"https://openalex.org/W7212008365","doi":"https://doi.org/10.48550/arxiv.2609.06297","title":"On the Matlis Reflexive Modules","display_name":"On the Matlis Reflexive Modules","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7212008365","doi":"https://doi.org/10.48550/arxiv.2609.06297"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06297","pdf_url":"https://arxiv.org/pdf/2609.06297","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.06297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066312963","display_name":"Behruz Sadeqi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210151143","display_name":"Islamic Azad University of Marand","ror":"https://ror.org/04rfmre55","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210151143"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Sadeqi, Behruz","raw_affiliation_strings":["Department of Mathematics , Mara.C. , Islamic Azad University Marand , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Mara.C. , Islamic Azad University Marand , Iran","institution_ids":["https://openalex.org/I4210151143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066312963"],"corresponding_institution_ids":["https://openalex.org/I4210151143"],"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.7958999872207642,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.7958999872207642,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.19470000267028809,"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":0.004399999976158142,"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/matlis-duality","display_name":"Matlis duality","score":0.8980000019073486},{"id":"https://openalex.org/keywords/complete-local-rings","display_name":"complete local rings","score":0.7720000147819519},{"id":"https://openalex.org/keywords/krull-schmidt-categories","display_name":"Krull-Schmidt categories","score":0.8009999990463257},{"id":"https://openalex.org/keywords/minimax-modules","display_name":"minimax modules","score":0.9700000286102295},{"id":"https://openalex.org/keywords/pontryagin-duality","display_name":"Pontryagin duality","score":0.8889999985694885},{"id":"https://openalex.org/keywords/grothendieck-duality","display_name":"Grothendieck duality","score":0.8410000205039978},{"id":"https://openalex.org/keywords/change-of-rings","display_name":"change of rings","score":0.7929999828338623},{"id":"https://openalex.org/keywords/pure-injective-modules","display_name":"pure-injective modules","score":0.996999979019165},{"id":"https://openalex.org/keywords/artinian-modules","display_name":"Artinian modules","score":0.7289999723434448},{"id":"https://openalex.org/keywords/noetherian-modules","display_name":"Noetherian modules","score":0.9430000185966492}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7484999895095825},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.6280999779701233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5310999751091003},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5091000199317932},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.3684999942779541},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.3010999858379364},{"id":"https://openalex.org/C13200473","wikidata":"https://www.wikidata.org/wiki/Q2747831","display_name":"Reflexivity","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28049999475479126},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.27000001072883606},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06297","pdf_url":"https://arxiv.org/pdf/2609.06297","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.2609.06297","doi":"https://doi.org/10.48550/arxiv.2609.06297","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06297","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:2609.06297","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06297","pdf_url":"https://arxiv.org/pdf/2609.06297","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/W7212008365.pdf","grobid_xml":"https://content.openalex.org/works/W7212008365.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4395687288","https://openalex.org/W1802087468","https://openalex.org/W7214096289","https://openalex.org/W4402121111","https://openalex.org/W2067515396","https://openalex.org/W2004802839","https://openalex.org/W2171705693","https://openalex.org/W1799370598","https://openalex.org/W2279586811","https://openalex.org/W4415697211"],"abstract_inverted_index":{"Matlis":[0,6,47,62,92,108,137],"duality,":[1],"first":[2,101],"introduced":[3],"by":[4],"Eben":[5],"in":[7,19],"1958,":[8],"stands":[9],"as":[10],"one":[11],"of":[12,46,91,107,126,145,202],"the":[13,55,60,76,88,97,105,120,143],"most":[14],"elegant":[15],"and":[16,29,43,168,174,189,194,197,205],"powerful":[17],"tools":[18],"commutative":[20],"algebra,":[21],"establishing":[22],"a":[23,41,71,112,116,150,200],"striking":[24],"contravariant":[25],"equivalence":[26],"between":[27],"Artinian":[28],"Noetherian":[30,131,151],"modules":[31,49,52,110,125,139,147,193],"over":[32],"complete":[33,130],"local":[34,132,185],"rings.":[35],"In":[36],"this":[37],"paper,":[38],"we":[39,134],"undertake":[40],"thorough":[42],"systematic":[44],"investigation":[45],"reflexive":[48,109,138],"---":[50,115],"those":[51],"for":[53,124],"which":[54],"canonical":[56],"evaluation":[57],"homomorphism":[58],"into":[59],"double":[61],"dual":[63],"is":[64,155],"an":[65],"isomorphism.":[66],"Our":[67],"exposition":[68],"begins":[69],"with":[70,142,172,199],"detailed":[72],"historical":[73],"narrative,":[74],"tracing":[75],"intellectual":[77],"trajectory":[78],"from":[79,100],"classical":[80,121],"Pontryagin":[81],"duality":[82],"through":[83],"Grothendieck's":[84],"dualizing":[85],"complexes":[86],"to":[87,183,191],"modern":[89],"formulation":[90],"duality.":[93],"We":[94,157],"then":[95],"develop":[96],"core":[98],"theory":[99],"principles,":[102],"demonstrating":[103],"that":[104,118,136],"class":[106,144],"constitutes":[111],"Krull-Schmidt":[113],"category":[114],"result":[117],"generalizes":[119],"decomposition":[122],"theorems":[123],"finite":[127,169],"length.":[128],"Over":[129],"rings,":[133],"prove":[135],"coincide":[140],"precisely":[141],"minimax":[146],"(those":[148],"possessing":[149],"submodule":[152],"whose":[153],"quotient":[154],"Artinian).":[156],"establish":[158],"full":[159],"closure":[160],"properties,":[161],"including":[162],"stability":[163],"under":[164],"submodules,":[165],"quotients,":[166],"extensions,":[167],"direct":[170],"sums,":[171],"rigorous":[173],"self-contained":[175],"proofs.":[176],"The":[177],"paper":[178],"also":[179],"surveys":[180],"recent":[181],"applications":[182],"generalized":[184],"cohomology,":[186],"change-of-rings":[187],"results,":[188],"connections":[190],"pure-injective":[192],"linear":[195],"compactness,":[196],"concludes":[198],"discussion":[201],"open":[203],"problems":[204],"future":[206],"research":[207],"directions.":[208]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-10T00:00:00"}
