{"id":"https://openalex.org/W2064143133","doi":"https://doi.org/10.1137/0213047","title":"<i>n</i>-Rational Algebras I. Basic Properties and Free Algebras","display_name":"<i>n</i>-Rational Algebras I. Basic Properties and Free Algebras","publication_year":1984,"publication_date":"1984-11-01","ids":{"openalex":"https://openalex.org/W2064143133","doi":"https://doi.org/10.1137/0213047","mag":"2064143133"},"language":"en","primary_location":{"id":"doi:10.1137/0213047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213047","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5016407219","display_name":"Jean Gallier","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jean H. Gallier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016407219"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1491,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89233449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"4","first_page":"750","last_page":"775"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.993399977684021,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.7528982758522034},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7030360102653503},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6771717667579651},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5971451997756958},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5345420241355896},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5059975981712341},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4640950560569763},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43279367685317993},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4273642897605896},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.41792741417884827},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40024060010910034},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11548662185668945},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.10518285632133484}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7528982758522034},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7030360102653503},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6771717667579651},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5971451997756958},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5345420241355896},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5059975981712341},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4640950560569763},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43279367685317993},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4273642897605896},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.41792741417884827},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40024060010910034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11548662185668945},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.10518285632133484},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0213047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213047","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W127754453","https://openalex.org/W1492311822","https://openalex.org/W1588303924","https://openalex.org/W1638993118","https://openalex.org/W1648879120","https://openalex.org/W1972289972","https://openalex.org/W1984467134","https://openalex.org/W1988436966","https://openalex.org/W2007098021","https://openalex.org/W2012313512","https://openalex.org/W2023307455","https://openalex.org/W2042319653","https://openalex.org/W2050407768","https://openalex.org/W2056239109","https://openalex.org/W2061786858","https://openalex.org/W2066126160","https://openalex.org/W2066192277","https://openalex.org/W2068599721","https://openalex.org/W2077359248","https://openalex.org/W2077884383","https://openalex.org/W2078050093","https://openalex.org/W2137230613","https://openalex.org/W4210249530","https://openalex.org/W4211265583","https://openalex.org/W4212777788","https://openalex.org/W4213252762","https://openalex.org/W4236364473","https://openalex.org/W4240176614","https://openalex.org/W4251097190","https://openalex.org/W4252070225"],"related_works":["https://openalex.org/W2954167023","https://openalex.org/W2064351239","https://openalex.org/W2949665548","https://openalex.org/W2114983089","https://openalex.org/W2950188642","https://openalex.org/W2028676759","https://openalex.org/W1589204344","https://openalex.org/W2257471395","https://openalex.org/W1780530600","https://openalex.org/W1985541145"],"abstract_inverted_index":{"A":[0,91],"(strict)":[1],"hierarchy":[2],"of":[3,29,51,56,63,68,87],"algebras":[4,43,70],"in":[5,41,71],"which":[6],"only":[7],"certain":[8],"\u201cconstructive\u201d":[9],"chains":[10,35],"have":[11,37],"a":[12,85],"least":[13,38],"upper":[14,39],"bound":[15],"is":[16,99],"studied.":[17,90],"Such":[18],"algebras,":[19,65],"called":[20],"n-rational,":[21],"are":[22,44,89],"\u201cideal\u201d":[23],"interpretations":[24],"for":[25],"finite":[26],"recursion":[27,49],"schemes":[28,50],"higher":[30,52],"types.":[31,53],"Indeed,":[32],"the":[33,66],"constructive":[34],"that":[36],"bounds":[40],"these":[42,64],"obtained":[45],"by":[46],"unfolding":[47],"rational":[48],"Part":[54,74],"I":[55],"this":[57],"paper":[58],"deals":[59],"with":[60,94],"basic":[61],"properties":[62],"existence":[67],"free":[69],"particular.":[72],"In":[73],"II":[75],"[SIAM":[76],"J.":[77],"Comput.,":[78],"13":[79],"(1984),":[80],"pp.":[81],"776\u2013794.],":[82],"varieties":[83],"and":[84],"logic":[86],"inequalities":[88],"proof":[92],"system":[93],"one":[95],"infinitary":[96],"inference":[97],"rule":[98],"shown":[100],"to":[101],"be":[102],"complete.":[103]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}