{"id":"https://openalex.org/W7214609352","doi":"https://doi.org/10.48550/arxiv.2609.30638","title":"Structure of irreducible homomorphisms to/from free and injective modules","display_name":"Structure of irreducible homomorphisms to/from free and injective modules","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214609352","doi":"https://doi.org/10.48550/arxiv.2609.30638"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30638","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30638","pdf_url":"https://arxiv.org/pdf/2609.30638","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/2609.30638","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065735894","display_name":"Saeed Nasseh","orcid":"https://orcid.org/0000-0002-5100-6969","observed_orcids":["https://orcid.org/0000-0002-5100-6969"]},"institutions":[{"id":"https://openalex.org/I39815113","display_name":"Georgia Southern University","ror":"https://ror.org/04agmb972","country_code":"US","type":"education","lineage":["https://openalex.org/I39815113"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nasseh, Saeed","raw_affiliation_strings":["Department of Mathematical Sciences , Georgia Southern University , Statesboro , GA 30460 , U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Georgia Southern University , Statesboro , GA 30460 , U.S.A","institution_ids":["https://openalex.org/I39815113"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065735894"],"corresponding_institution_ids":["https://openalex.org/I39815113"],"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":0.6869999766349792,"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":0.6869999766349792,"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":0.25369998812675476,"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":0.04430000111460686,"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/free-modules","display_name":"free modules","score":0.9330000281333923},{"id":"https://openalex.org/keywords/injective-modules","display_name":"injective modules","score":1.0},{"id":"https://openalex.org/keywords/finitely-generated-modules","display_name":"finitely generated modules","score":0.8870000243186951},{"id":"https://openalex.org/keywords/artinian-modules","display_name":"Artinian modules","score":0.8519999980926514},{"id":"https://openalex.org/keywords/commutative-noetherian-local-rings","display_name":"commutative Noetherian local rings","score":0.925000011920929},{"id":"https://openalex.org/keywords/complete-local-rings","display_name":"complete local rings","score":0.921999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904999852180481},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6863999962806702},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6571999788284302},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5759000182151794},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.49900001287460327},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C99463465","wikidata":"https://www.wikidata.org/wiki/Q2716519","display_name":"Injective module","level":3,"score":0.4693000018596649},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.4180000126361847},{"id":"https://openalex.org/C35729967","wikidata":"https://www.wikidata.org/wiki/Q18848","display_name":"Module","level":4,"score":0.36250001192092896},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.35040000081062317},{"id":"https://openalex.org/C154441711","wikidata":"https://www.wikidata.org/wiki/Q1782332","display_name":"Divisible group","level":5,"score":0.3395000100135803},{"id":"https://openalex.org/C100036529","wikidata":"https://www.wikidata.org/wiki/Q1945067","display_name":"Monomorphism","level":3,"score":0.3301999866962433},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3269999921321869},{"id":"https://openalex.org/C106387445","wikidata":"https://www.wikidata.org/wiki/Q1485102","display_name":"Semisimple module","level":4,"score":0.31679999828338623},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C32268108","wikidata":"https://www.wikidata.org/wiki/Q942423","display_name":"Projective module","level":3,"score":0.30640000104904175},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28200000524520874},{"id":"https://openalex.org/C134565946","wikidata":"https://www.wikidata.org/wiki/Q906015","display_name":"Direct limit","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30638","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30638","pdf_url":"https://arxiv.org/pdf/2609.30638","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.2609.30638","doi":"https://doi.org/10.48550/arxiv.2609.30638","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30638","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":"pmh:oai:arXiv.org:2609.30638","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30638","pdf_url":"https://arxiv.org/pdf/2609.30638","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/W7214609352.pdf","grobid_xml":"https://content.openalex.org/works/W7214609352.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2963084855","https://openalex.org/W2023778781","https://openalex.org/W2016783131","https://openalex.org/W1965683465","https://openalex.org/W2069755371","https://openalex.org/W2793294098","https://openalex.org/W4401246843","https://openalex.org/W2071088390","https://openalex.org/W1988399607","https://openalex.org/W4288519188"],"abstract_inverted_index":{"Let":[0],"$R$":[1,39],"be":[2],"a":[3],"commutative":[4],"noetherian":[5],"local":[6],"ring.":[7],"We":[8],"extend":[9],"the":[10,13,19,29,36,45,58],"work":[11],"of":[12,21,31,47,60],"author":[14],"and":[15,50,53],"Takahashi":[16],"by":[17],"investigating":[18],"structure":[20,46],"irreducible":[22,48],"monomorphisms":[23,49],"originating":[24],"from":[25,54],"free":[26],"modules":[27,56],"in":[28,57],"category":[30,59],"finitely":[32],"generated":[33],"$R$-modules.":[34,62],"In":[35],"case":[37],"where":[38],"is":[40],"complete,":[41],"we":[42],"further":[43],"study":[44],"epimorphisms":[51],"to":[52],"injective":[55],"artinian":[61]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-29T00:00:00"}