{"id":"https://openalex.org/W2088134129","doi":"https://doi.org/10.2178/jsl/1268917489","title":"Strongly and co-strongly minimal abelian structures","display_name":"Strongly and co-strongly minimal abelian structures","publication_year":2010,"publication_date":"2010-03-18","ids":{"openalex":"https://openalex.org/W2088134129","doi":"https://doi.org/10.2178/jsl/1268917489","mag":"2088134129"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1268917489","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1268917489","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053070582","display_name":"Ehud Hrushovski","orcid":"https://orcid.org/0000-0002-2761-6513"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ehud Hrushovski","raw_affiliation_strings":["Department of Mathematicc, Hebrew University at Jerusalem, 91904 Jerusalem, Israel. E-mail:","Hebrew University at Jerusalem"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematicc, Hebrew University at Jerusalem, 91904 Jerusalem, Israel. E-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Hebrew University at Jerusalem","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060022064","display_name":"James Loveys","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"James Loveys","raw_affiliation_strings":["The Department of Mathematics and Statistics, Mcgill University, Burnside Hall, Room 916, 805 Sherbrooke W. Montreal, Qc, H3A 2K6, Canada. E-mail:","McGill University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Department of Mathematics and Statistics, Mcgill University, Burnside Hall, Room 916, 805 Sherbrooke W. Montreal, Qc, H3A 2K6, Canada. E-mail:","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"McGill University","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5295,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64518556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"75","issue":"2","first_page":"442","last_page":"458"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9995999932289124,"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":0.9995999932289124,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9979000091552734,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.7420462369918823},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7246512770652771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6932600736618042},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5954776406288147},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5878657102584839},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5145453810691833},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5099278688430786},{"id":"https://openalex.org/keywords/division-ring","display_name":"Division ring","score":0.4831644892692566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4453229308128357},{"id":"https://openalex.org/keywords/elementary-abelian-group","display_name":"Elementary abelian group","score":0.42364686727523804},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3899686634540558},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.23175102472305298},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13440698385238647},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.06991374492645264}],"concepts":[{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.7420462369918823},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7246512770652771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6932600736618042},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5954776406288147},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5878657102584839},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5145453810691833},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5099278688430786},{"id":"https://openalex.org/C31671303","wikidata":"https://www.wikidata.org/wiki/Q650741","display_name":"Division ring","level":3,"score":0.4831644892692566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4453229308128357},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.42364686727523804},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3899686634540558},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.23175102472305298},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13440698385238647},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.06991374492645264}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1268917489","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1268917489","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1268917489","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1268917489","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W122231","https://openalex.org/W134345042","https://openalex.org/W1522423813","https://openalex.org/W1577003333","https://openalex.org/W1993603861","https://openalex.org/W1998136456","https://openalex.org/W2005548999","https://openalex.org/W2046056764","https://openalex.org/W2127469771","https://openalex.org/W2153211620","https://openalex.org/W2283058393"],"related_works":["https://openalex.org/W4236834764","https://openalex.org/W4246811655","https://openalex.org/W2042334973","https://openalex.org/W4320035820","https://openalex.org/W2391321755","https://openalex.org/W2127530926","https://openalex.org/W2377983882","https://openalex.org/W2058919198","https://openalex.org/W2120157773","https://openalex.org/W2089940022"],"abstract_inverted_index":{"Abstract":[0],"We":[1,165],"give":[2,24],"several":[3],"characterizations":[4],"of":[5,53,72,90,93,95,115,133,139,156,177],"weakly":[6,170,179],"minimal":[7,47,171,180],"abelian":[8,66,172],"structures.":[9],"In":[10,59,108],"two":[11],"special":[12],"cases,":[13],"dual":[14],"in":[15,98,161],"a":[16,69,73,78,118,137,142,175,178],"sense":[17],"to":[18,102],"be":[19],"made":[20],"explicit":[21],"below,":[22],"we":[23,63],"precise":[25],"structure":[26,55,67,112,130,173],"theorems:":[27],"1.":[28],"when":[29,50],"the":[30,41,51,54,60,65,109,111,126,154],"only":[31,42,127],"finite":[32,96],"0-definable":[33],"subgroup":[34,143],"is":[35,40,56,113,141,163,174],"{0},":[36],"or":[37],"equivalently":[38],"0":[39],"algebraic":[43],"element":[44],"(the":[45],"co-strongly":[46],"case);":[48],"2.":[49],"theory":[52],"strongly":[57],"minimal.":[58],"first":[61],"case,":[62],"identify":[64],"as":[68,123],"\u201cnear-subspace\u201d":[70],"A":[71,94,99,144,157,162],"vector":[74,119],"space":[75,120],"V":[76,140],"over":[77],"division":[79],"ring":[80],"D":[81,152],"with":[82,86,125],"its":[83],"induced":[84],"structure,":[85],"possibly":[87],"some":[88,131],"collection":[89,132],"distinguished":[91,134],"subgroups":[92],"index":[97,155],"and":[100,121],"(up":[101],"acl":[103],"(\u2205))":[104],"no":[105],"further":[106,128],"structure.":[107],"second,":[110],"that":[114,146,168],"V/A":[116],"for":[117,147],"near-subspace":[122,138],"above,":[124],"possible":[129],"points.":[135],"Here":[136],"such":[145],"any":[148,169],"nonzero":[149],"d":[150],"\u2208":[151],".":[153],"\u2229":[158],"dA":[159],",":[160],"finite.":[164],"also":[166],"show":[167],"reduct":[176],"module.":[181]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}