{"id":"https://openalex.org/W2007581493","doi":"https://doi.org/10.1145/1089235.1089238","title":"A simplified proof of the characterization theorem for Gr\u00f6bner-bases","display_name":"A simplified proof of the characterization theorem for Gr\u00f6bner-bases","publication_year":1980,"publication_date":"1980-11-01","ids":{"openalex":"https://openalex.org/W2007581493","doi":"https://doi.org/10.1145/1089235.1089238","mag":"2007581493"},"language":"en","primary_location":{"id":"doi:10.1145/1089235.1089238","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1089235.1089238","pdf_url":null,"source":{"id":"https://openalex.org/S4210226623","display_name":"ACM SIGSAM Bulletin","issn_l":"0163-5824","issn":["0163-5824","1557-9492"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGSAM Bulletin","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/A5090703131","display_name":"Leo Bachmair","orcid":null},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"L. Bachmair","raw_affiliation_strings":["Johannes Kepler Universit\u00e4t, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler Universit\u00e4t, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017274120","display_name":"Bruno Buchberger","orcid":null},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"B. Buchberger","raw_affiliation_strings":["Johannes Kepler Universit\u00e4t, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler Universit\u00e4t, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090703131"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":1.0929,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.75412057,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"4","first_page":"29","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9884999990463257,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9884999990463257,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9653000235557556,"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/mathematics","display_name":"Mathematics","score":0.8557958602905273},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6803935170173645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5140989422798157},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.47000083327293396},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4426475763320923},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4328126311302185},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.42362871766090393},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41393494606018066},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.376251757144928}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8557958602905273},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6803935170173645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5140989422798157},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.47000083327293396},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4426475763320923},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4328126311302185},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.42362871766090393},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41393494606018066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.376251757144928},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1089235.1089238","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1089235.1089238","pdf_url":null,"source":{"id":"https://openalex.org/S4210226623","display_name":"ACM SIGSAM Bulletin","issn_l":"0163-5824","issn":["0163-5824","1557-9492"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGSAM Bulletin","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1481997196","https://openalex.org/W1968386045","https://openalex.org/W2007704220","https://openalex.org/W2018615018","https://openalex.org/W2098036931","https://openalex.org/W4233685614"],"related_works":["https://openalex.org/W4280511095","https://openalex.org/W4287734682","https://openalex.org/W2009896212","https://openalex.org/W3101324537","https://openalex.org/W4210984194","https://openalex.org/W4312183672","https://openalex.org/W2952659830","https://openalex.org/W140161291","https://openalex.org/W3092492263","https://openalex.org/W2964204291"],"abstract_inverted_index":{"In":[0],"/2/":[1],"a":[2,21,52,65,93,101,119],"certain":[3],"type":[4],"of":[5,23,30,38,40,49,80,100,110],"bases":[6,39],"(\"Gr\u00f6bner-Bases\")":[7],"for":[8,55],"polynomial":[9,31,94],"ideals":[10,32],"has":[11],"been":[12],"introduced":[13],"whose":[14,57],"usefulness":[15],"stems":[16],"from":[17],"the":[18,28,36,89,97,108,129],"fact":[19],"that":[20,78],"number":[22],"important":[24],"computability":[25],"problems":[26],"in":[27,59,83,107],"theory":[29],"are":[33,79],"reducible":[34],"to":[35,45,127],"construction":[37,48],"this":[41,63],"type.":[42],"The":[43,70,85,115],"key":[44],"an":[46],"algorithmic":[47],"Gr\u00f6bner-bases":[50,56,111],"is":[51,68,72,118],"characterization":[53],"theorem":[54],"proof":[58,67],"/2/is":[60],"rather":[61],"complex.In":[62],"paper":[64],"simplified":[66],"given.":[69],"simplification":[71],"based":[73],"on":[74,121],"two":[75],"new":[76],"lemmas":[77],"some":[81],"interest":[82],"themselves.":[84],"first":[86],"lemma":[87,117,120],"characterizes":[88],"congruence":[90],"relation":[91,104],"modulo":[92],"ideal":[95],"as":[96],"reflexive-transitive":[98],"closure":[99],"particular":[102],"reduction":[103,123],"(\"M-reduction\")":[105],"used":[106],"definition":[109],"and":[112],"its":[113],"inverse.":[114],"second":[116],"general":[122],"relations,":[124],"which":[125],"allows":[126],"guarantee":[128],"Church-Rosser":[130],"property":[131],"under":[132],"very":[133],"weak":[134],"assumptions.":[135]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
