{"id":"https://openalex.org/W2085627734","doi":"https://doi.org/10.1305/ndjfl/1093635235","title":"An isomorphism between rings and groups.","display_name":"An isomorphism between rings and groups.","publication_year":1989,"publication_date":"1989-09-01","ids":{"openalex":"https://openalex.org/W2085627734","doi":"https://doi.org/10.1305/ndjfl/1093635235","mag":"2085627734"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093635235","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093635235","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-30/issue-4/An-isomorphism-between-rings-and-groups/10.1305/ndjfl/1093635235.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-30/issue-4/An-isomorphism-between-rings-and-groups/10.1305/ndjfl/1093635235.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014665452","display_name":"Awad A. Iskander","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Awad A. Iskander","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014665452"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28435115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.17900000512599945,"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":0.17900000512599945,"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/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7480085492134094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4883250892162323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43090540170669556},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3834575414657593},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.13586890697479248},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.11194688081741333},{"id":"https://openalex.org/keywords/crystal-structure","display_name":"Crystal structure","score":0.07959401607513428}],"concepts":[{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7480085492134094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4883250892162323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43090540170669556},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3834575414657593},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.13586890697479248},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.11194688081741333},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.07959401607513428}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093635235","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093635235","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-30/issue-4/An-isomorphism-between-rings-and-groups/10.1305/ndjfl/1093635235.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093635235","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093635235","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":{"id":"doi:10.1305/ndjfl/1093635235","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093635235","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-30/issue-4/An-isomorphism-between-rings-and-groups/10.1305/ndjfl/1093635235.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2085627734.pdf","grobid_xml":"https://content.openalex.org/works/W2085627734.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4253601112","https://openalex.org/W4293176479","https://openalex.org/W6818243615"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Bijective":[0],"functors":[1],"\u03c3":[2],"and":[3,15,29,36,87,167,238],"p":[4],"are":[5,75,128,135,203,281,293,296],"constructed":[6],"between":[7],"a":[8,16,43,50,57,115,182,249,303],"category":[9,17],"(R":[10],"of":[11,19,45,69,78,100,126,142,145,151,170,184,199,208,222,241,251,273,283,289,298,305,307,312,322,327],"commutative":[12],"nonassociative":[13],"rings":[14,175,200],"9":[18],"nilpotent":[20,102,160,185,209,231,252],"groups,":[21],"such":[22],"that":[23,66,97,148,196,267,276,292,329],"for":[24],"all":[25,101,171,242,325],"R":[26,35],"e":[27],"<R":[28],"G":[30,31],"S,":[32],"P\u00b0R":[33],"=":[34,38],"\u03c3pG":[37],"G.Furthermore,":[39],"if":[40],"\u00a3":[41],"is":[42,154,178,214,225,245,268],"subclass":[44],"(R,":[46],"then":[47,131],"<\u00a3":[48],"has":[49,56,107],"decidable":[51,58],"elementary":[52,59,73,110,133,320],"theory":[53,275,291,321],"iff":[54],"\u03c3<\u00a3":[55],"theory.Among":[60],"the":[61,76,98,143,149,158,168,191,220,229,239,287],"methods":[62],"used":[63,92,279,294],"to":[64,95,157,181,206,228,248],"prove":[65],"certain":[67,197],"classes":[68,125,198,207],"models":[70,127,306],"have":[71],"undecidable":[72,109,138],"theories":[74,134],"\"interpretation":[77],"one":[79],"class":[80,99,103,161,169,183,186,213,232,240,250,253,304],"into":[81],"another\"":[82],"(cf.[7]),":[83],"\"semantic":[84],"embedding\"":[85],"(cf.[1]),":[86],"\"syntactic":[88,93,122],"inclusion\"":[89,94],"(cf.[3]).MaFcev":[90],"[3]":[91,146],"show":[96,195],"Az-groups":[104],"(for":[105],"n>2)":[106],"an":[108],"theory.In":[111],"fact,":[112],"MaPcev":[113],"employed":[114],"notion":[116],"which":[117],"we":[118,194],"will":[119,258,277,315],"here":[120,280,295],"call":[121],"isomorphism\".If":[123],"two":[124,164,189,235],"syntactically":[129,155,179,204,226,246],"isomorphic,":[130],"their":[132],"either":[136],"simultaneously":[137,140],"or":[139],"decidable.One":[141],"results":[144],"states":[147],"ring":[150,221,261],"integers":[152,223],"Z":[153,224],"isomorphic":[156,180,205,227,247],"free":[159,165,230,236],"2-group":[162],"on":[163],"generators,":[166,237],"not":[172,269],"necessarily":[173,270],"associative":[174],"with":[176,188,201,234,262],"identity":[177,202,263],"2-groups":[187],"constants.In":[190],"present":[192],"paper,":[193],"groups":[210],"whose":[211],"nilpotency":[212],"at":[215],"most":[216],"3;":[217],"in":[218],"particular,":[219],"3-group":[233],"Boolean":[243],"algebras":[244],"2-groups.The":[254],"phrase":[255],"\"nonassociative":[256],"ring\"":[257],"mean":[259],"\"a":[260],"(denoted":[264],"by":[265,318],"1)":[266],"associative\".The":[271],"notations":[272,288],"decidability":[274],"be":[278,302,316],"those":[282,297],"[7].Unless":[284],"otherwise":[285],"stated,":[286],"group":[290],"[4].":[299],"/Let":[300],"JC":[301],"type":[308,313],"r.The":[309],"first-order":[310],"language":[311],"\u03c4":[314],"denoted":[317],"Lr.The":[319],"JC,":[323],"i.e.,":[324],"sentences":[326],"Lr":[328]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}