{"id":"https://openalex.org/W4410909148","doi":"https://doi.org/10.1007/s10485-025-09814-2","title":"Vop\u011bnka\u2019s Principle, Maximum Deconstructibility, and Singly-Generated Torsion Classes","display_name":"Vop\u011bnka\u2019s Principle, Maximum Deconstructibility, and Singly-Generated Torsion Classes","publication_year":2025,"publication_date":"2025-05-31","ids":{"openalex":"https://openalex.org/W4410909148","doi":"https://doi.org/10.1007/s10485-025-09814-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-025-09814-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09814-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-025-09814-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10485-025-09814-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055954499","display_name":"Sean Cox","orcid":"https://orcid.org/0000-0001-5546-7079"},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sean Cox","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond, VA, 23284, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond, VA, 23284, USA","institution_ids":["https://openalex.org/I184840846"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055954499"],"corresponding_institution_ids":["https://openalex.org/I184840846"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":{"value":3290,"currency":"USD","value_usd":3290},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16587356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9994999766349792,"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":0.9980999827384949,"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":0.9937999844551086,"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/torsion","display_name":"Torsion (gastropod)","score":0.6849694848060608},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6181908249855042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5040949583053589},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3236779570579529},{"id":"https://openalex.org/keywords/anatomy","display_name":"Anatomy","score":0.19929733872413635},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1574172079563141},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11221545934677124}],"concepts":[{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.6849694848060608},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6181908249855042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5040949583053589},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3236779570579529},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.19929733872413635},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1574172079563141},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11221545934677124}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10485-025-09814-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09814-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-025-09814-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10485-025-09814-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09814-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-025-09814-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8362975237","display_name":"Approximation Theory and Elementary Submodels","funder_award_id":"2154141","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410909148.pdf","grobid_xml":"https://content.openalex.org/works/W4410909148.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1590477903","https://openalex.org/W1595870841","https://openalex.org/W1966101132","https://openalex.org/W1976465084","https://openalex.org/W1991438135","https://openalex.org/W1997385275","https://openalex.org/W2041043898","https://openalex.org/W2073596159","https://openalex.org/W2075424595","https://openalex.org/W2112425798","https://openalex.org/W2114145385","https://openalex.org/W2162821231","https://openalex.org/W2238934968","https://openalex.org/W2295988358","https://openalex.org/W2578931604","https://openalex.org/W2889091071","https://openalex.org/W2963401956","https://openalex.org/W2963843942","https://openalex.org/W2963909885","https://openalex.org/W3005764267","https://openalex.org/W3088881935","https://openalex.org/W3211093699","https://openalex.org/W4232255678","https://openalex.org/W4300662053","https://openalex.org/W4403457743","https://openalex.org/W4403996425"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"Deconstructibility":[1,30],"is":[2,44,96,112],"an":[3,86],"often-used":[4],"sufficient":[5],"condition":[6,37],"on":[7],"a":[8,34,39,115,125],"class":[9,40,108,120],"$$\\mathcal":[10,24],"{C}$$":[11,25],"of":[12,54,85,109,124,127],"modules":[13],"that":[14,33,51,94,105],"allows":[15],"one":[16],"to":[17,23,41,76,98,102],"carry":[18],"out":[19],"homological":[20],"algebra":[21],"relative":[22],".":[26],"The":[27],"principle":[28],"Maximum":[29],"(MD)":[31],"asserts":[32],"certain":[35],"necessary":[36],"for":[38,49],"be":[42],"deconstructible":[43,69],"also":[45],"sufficient.":[46],"MD":[47,73,95],"implies,":[48],"example,":[50],"the":[52,83,103,119,122],"classes":[53,67],"Gorenstein":[55],"Projective":[56,59],"modules,":[57,60],"Ding":[58],"their":[61],"relativized":[62],"variants,":[63],"and":[64,81,101,129],"all":[65],"torsion":[66,107],"are":[68],"over":[70],"any":[71],"ring.":[72],"was":[74],"known":[75],"follow":[77],"from":[78],"Vop\u011bnka\u2019s":[79,99],"Principle":[80],"imply":[82],"existence":[84],"$$\\omega":[87],"_1$$":[88],"-strongly":[89],"compact":[90],"cardinal.":[91],"We":[92],"prove":[93],"equivalent":[97],"Principle,":[100],"assertion":[104],"each":[106],"abelian":[110],"groups":[111],"generated":[113],"by":[114],"single":[116],"group":[117],"within":[118],"(yielding":[121],"converse":[123],"theorem":[126],"G\u00f6bel":[128],"Shelah).":[130]},"counts_by_year":[],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}