{"id":"https://openalex.org/W1996757555","doi":"https://doi.org/10.2178/jsl/1190150153","title":"The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group","display_name":"The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W1996757555","doi":"https://doi.org/10.2178/jsl/1190150153","mag":"1996757555"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150153","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150153","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":"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/A5026525806","display_name":"Annalisa Marcja","orcid":null},"institutions":[{"id":"https://openalex.org/I4402554200","display_name":"Liceo scientifico statale Ulisse Dini","ror":"https://ror.org/006xg2x43","country_code":null,"type":"education","lineage":["https://openalex.org/I4402554200"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Marcja","raw_affiliation_strings":["Dipartimento Di Matematica, U. Dini, Universit\u00e0 Di Firenze, Viale Morgagni 67/A, 1-50134 Firenze, Italy, E-mail:","Dipartimento Di Matematica, U. Dini, Universit\u00e0 Di Firenze, Viale Morgagni 67/A, 1-50134 Firenze, Italy, E-mail: marcja@math.unifi.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento Di Matematica, U. Dini, Universit\u00e0 Di Firenze, Viale Morgagni 67/A, 1-50134 Firenze, Italy, E-mail:","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dipartimento Di Matematica, U. Dini, Universit\u00e0 Di Firenze, Viale Morgagni 67/A, 1-50134 Firenze, Italy, E-mail: marcja@math.unifi.it","institution_ids":["https://openalex.org/I4402554200","https://openalex.org/I45084792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012013257","display_name":"Mike Prest","orcid":"https://orcid.org/0000-0002-8723-623X"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"M. Prest","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England, E-mail:","Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England, E-mail: mprest@ma.man.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England, E-mail:","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England, E-mail: mprest@ma.man.ac.uk","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011521416","display_name":"Carlo Toffalori","orcid":"https://orcid.org/0000-0002-5570-8597"},"institutions":[{"id":"https://openalex.org/I112859197","display_name":"Universit\u00e0 di Camerino","ror":"https://ror.org/0005w8d69","country_code":"IT","type":"education","lineage":["https://openalex.org/I112859197"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"C. Toffalori","raw_affiliation_strings":["Dipartimento Di Matematica E Infomatica, Universit\u00e0 Di Camerino, Via Madonna Delle Carceri, 1-62032 Camerino, Italy, E-mail:","Dipartimento Di Matematica E Infomatica, Universit\u00e0 Di Camerino, Via Madonna Delle Carceri, 1-62032 Camerino, Italy, E-mail: carlo.toffalori@unicam.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento Di Matematica E Infomatica, Universit\u00e0 Di Camerino, Via Madonna Delle Carceri, 1-62032 Camerino, Italy, E-mail:","institution_ids":["https://openalex.org/I112859197"]},{"raw_affiliation_string":"Dipartimento Di Matematica E Infomatica, Universit\u00e0 Di Camerino, Via Madonna Delle Carceri, 1-62032 Camerino, Italy, E-mail: carlo.toffalori@unicam.it","institution_ids":["https://openalex.org/I112859197"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.4648,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.5778498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"3","first_page":"1126","last_page":"1140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9993000030517578,"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":0.9993000030517578,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.5721151828765869},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.5453514456748962},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5058988928794861},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.48237887024879456},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.45826584100723267},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.454184889793396},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.45297330617904663},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4379216432571411},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4275813400745392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36309558153152466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32791438698768616},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11313378810882568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5721151828765869},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.5453514456748962},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5058988928794861},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.48237887024879456},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.45826584100723267},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.454184889793396},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.45297330617904663},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4379216432571411},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4275813400745392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36309558153152466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32791438698768616},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11313378810882568},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1190150153","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150153","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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150153","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150153","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W35836478","https://openalex.org/W1535506975","https://openalex.org/W1577003333","https://openalex.org/W1596298884","https://openalex.org/W1999220295","https://openalex.org/W2068962640","https://openalex.org/W2069988671","https://openalex.org/W2077736462","https://openalex.org/W2153211620","https://openalex.org/W2283058393","https://openalex.org/W2327816196","https://openalex.org/W4213088535","https://openalex.org/W4256141017"],"related_works":["https://openalex.org/W4237107081","https://openalex.org/W3105245946","https://openalex.org/W2060542026","https://openalex.org/W2264022753","https://openalex.org/W2386314338","https://openalex.org/W3200309776","https://openalex.org/W2354689617","https://openalex.org/W2389993406","https://openalex.org/W2376584285","https://openalex.org/W1510249257"],"abstract_inverted_index":{"For":[0,107],"every":[1,108],"ring":[2,217,235],"S":[3,73,120,145],"with":[4,33,249],"identity,":[5],"the":[6,16,34,50,66,82,100,130,136,175,184,209,234,250,264],"(right)":[7,25],"Ziegler":[8,28,101,176,185,210],"spectrum":[9,211],"of":[10,18,36,49,110,135,183,214,226,237,254,266],"S,":[11],"Zg":[12,31,85,104,140,171,212,255],"s":[13,32,71,86,105,141,172],",":[14,128,219],"is":[15,48,94,187,222,241,263],"set":[17,44,84,131],"(isomorphism":[19],"classes":[20],"of)":[21],"indecomposable":[22],"pure":[23],"injective":[24],"S-modules.":[26],"The":[27,167,178,258],"topology":[29,47,102,169,186],"equips":[30],"structure":[35],"a":[37,163,215,223,242],"topological":[38],"space.":[39],"A":[40,125,149],"typical":[41],"basic":[42,164],"open":[43,165],"in":[45,65,139,189,193,208],"this":[46,262],"form":[51],"where":[52,220],"\u03c6":[53,77,89],"and":[54,118,180,192,200,239],"\u03c8":[55,79,91],"are":[56,206],"pp":[57],"-formulas":[58],"(with":[59],"at":[60],"most":[61],"one":[62],"free":[63],"variable)":[64],"first":[67],"order":[68],"language":[69],"L":[70],"for":[72,202,261],"-modules;":[74],"let":[75],"[":[76],"/":[78,90],"]":[80],"denote":[81],"closed":[83],"-":[87],"(":[88,132,159],").":[92],"There":[93],"an":[95,119],"alternative":[96],"way":[97],"to":[98],"introduce":[99],"on":[103,170],".":[106,157,257],"choice":[109],"two":[111],"f.p.":[112],"(finitely":[113],"presented)":[114],"S-modules":[115],"A,":[116],"B":[117,127],"-module":[121],"homomorphism":[122],"f":[123,133,156,160],":":[124,148],"\u2192":[126,150],"consider":[129],")":[134,161],"points":[137,253],"N":[138,151],"such":[142],"that":[143],"some":[144],"-homomorphism":[146],"h":[147],"does":[152],"not":[153],"factor":[154],"through":[155],"Take":[158],"as":[162],"set.":[166],"resulting":[168],"is,":[173],"again,":[174],"topology.":[177],"algebraic":[179],"model-theoretic":[181],"relevance":[182],"discussed":[188],"[Z],":[190],"[P]":[191],"many":[194],"subsequent":[195],"papers,":[196],"including":[197],"[P1],":[198],"[P2]":[199],"[P3],":[201],"instance.":[203],"Here":[204],"we":[205,247],"interested":[207],"RG":[213,218,256,267,274],"group":[216],"R":[221,231,251,272],"Dedekind":[224],"domain":[225],"characteristic":[227],"0":[228],"(for":[229],"example":[230],"could":[232],"be":[233],"Z":[236],"integers)":[238],"G":[240],"finite":[243],"group.":[244],"In":[245],"particular":[246],"deal":[248],"-torsionfree":[252,273],"main":[259],"motivation":[260],"study":[265],"-lattices":[268],"(i.e.,":[269],"finitely":[270],"generated":[271],"-modules).":[275]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
