{"id":"https://openalex.org/W4415991300","doi":"https://doi.org/10.3390/axioms14110824","title":"Weak Resolution Dimensions of Subcategories","display_name":"Weak Resolution Dimensions of Subcategories","publication_year":2025,"publication_date":"2025-11-07","ids":{"openalex":"https://openalex.org/W4415991300","doi":"https://doi.org/10.3390/axioms14110824"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14110824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110824","pdf_url":"https://www.mdpi.com/2075-1680/14/11/824/pdf?version=1762504310","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/2075-1680/14/11/824/pdf?version=1762504310","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058659573","display_name":"Juxiang Sun","orcid":"https://orcid.org/0009-0003-0214-100X"},"institutions":[{"id":"https://openalex.org/I89381930","display_name":"Shangqiu Normal University","ror":"https://ror.org/008m8sh03","country_code":"CN","type":"education","lineage":["https://openalex.org/I89381930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juxiang Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China"],"raw_orcid":"https://orcid.org/0009-0003-0214-100X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China","institution_ids":["https://openalex.org/I89381930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115595085","display_name":"Xinpeng Liu","orcid":"https://orcid.org/0000-0002-9558-180X"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xinpeng Liu","raw_affiliation_strings":["School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112111335","display_name":"Weimin Liu","orcid":"https://orcid.org/0000-0001-7507-6032"},"institutions":[{"id":"https://openalex.org/I89381930","display_name":"Shangqiu Normal University","ror":"https://ror.org/008m8sh03","country_code":"CN","type":"education","lineage":["https://openalex.org/I89381930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weimin Liu","raw_affiliation_strings":["Department of Physics, Shangqiu Normal University, Shangqiu 476000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Shangqiu Normal University, Shangqiu 476000, China","institution_ids":["https://openalex.org/I89381930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112111335"],"corresponding_institution_ids":["https://openalex.org/I89381930"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.39809649,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"11","first_page":"824","last_page":"824"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.41280001401901245,"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":0.41280001401901245,"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":0.21789999306201935,"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":0.19979999959468842,"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/resolution","display_name":"Resolution (logic)","score":0.6700999736785889},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5519000291824341},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5414000153541565},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46320000290870667},{"id":"https://openalex.org/keywords/semisimple-module","display_name":"Semisimple module","score":0.439300000667572},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.38909998536109924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7943999767303467},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.6700999736785889},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5625},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5519000291824341},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5414000153541565},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C106387445","wikidata":"https://www.wikidata.org/wiki/Q1485102","display_name":"Semisimple module","level":4,"score":0.439300000667572},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.336899995803833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C149774684","wikidata":"https://www.wikidata.org/wiki/Q713084","display_name":"Artinian ring","level":4,"score":0.28040000796318054},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2720000147819519}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14110824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110824","pdf_url":"https://www.mdpi.com/2075-1680/14/11/824/pdf?version=1762504310","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:doaj.org/article:0aae60ecf1b0483f8e03556c234a43b7","is_oa":true,"landing_page_url":"https://doaj.org/article/0aae60ecf1b0483f8e03556c234a43b7","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,"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":"Axioms, Vol 14, Iss 11, p 824 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14110824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110824","pdf_url":"https://www.mdpi.com/2075-1680/14/11/824/pdf?version=1762504310","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415991300.pdf","grobid_xml":"https://content.openalex.org/works/W4415991300.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1509436520","https://openalex.org/W2003904750","https://openalex.org/W2043179951","https://openalex.org/W2076992376","https://openalex.org/W2150194480","https://openalex.org/W3160736052","https://openalex.org/W4402439558"],"related_works":[],"abstract_inverted_index":{"We":[0,53],"investigate":[1],"the":[2,5,18,56,66,69],"relationships":[3],"between":[4],"weak":[6,57,82],"resolution":[7,58,83],"dimensions":[8,71,84],"of":[9,11,14,33,60,68,85],"subcategories":[10,32],"module":[12],"categories":[13],"Artinian":[15,25,86],"algebras":[16,87],"in":[17,40],"present":[19],"paper.":[20],"Let":[21],"\u039b":[22],"be":[23],"an":[24,45],"algebra,":[26],"and":[27,30,51,74,92],"A,":[28],"B":[29,75],"X":[31,39,41,61],"\u039b-modules,":[34],"such":[35],"that":[36,55],"each":[37],"object":[38],"is":[42,62],"given":[43],"by":[44,65],"exact":[46],"sequence":[47],"0\u2192A\u2192B\u2192X\u21920":[48],"with":[49],"A\u2208ObA":[50],"B\u2208ObB.":[52],"prove":[54],"dimension":[59],"bounded":[63],"above":[64],"sum":[67],"corresponding":[70],"for":[72],"A":[73],"plus":[76],"1.":[77],"As":[78],"applications,":[79],"we":[80],"study":[81],"under":[88],"left":[89],"idealized":[90],"extensions":[91],"conditions":[93],"on":[94],"special":[95],"ideals.":[96]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-11-07T00:00:00"}
