{"id":"https://openalex.org/W2963646965","doi":"https://doi.org/10.1142/s0218196709005184","title":"NORMAL DOMAINS WITH MONOMIAL PRESENTATIONS","display_name":"NORMAL DOMAINS WITH MONOMIAL PRESENTATIONS","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2963646965","doi":"https://doi.org/10.1142/s0218196709005184","mag":"2963646965"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005184","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005184","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5006029720","display_name":"Isabel Goffa","orcid":null},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"ISABEL GOFFA","raw_affiliation_strings":["Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022675321","display_name":"Eric Jespers","orcid":"https://orcid.org/0000-0002-2695-7949"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"ERIC JESPERS","raw_affiliation_strings":["Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080398488","display_name":"Jan Okni\u0144ski","orcid":"https://orcid.org/0000-0002-2434-3425"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"JAN OKNI\u0143SKI","raw_affiliation_strings":["Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland","institution_ids":["https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006029720"],"corresponding_institution_ids":["https://openalex.org/I13469542"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39249055,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"03","first_page":"287","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998000264167786,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998000264167786,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9980999827384949,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.9067509770393372},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8645774126052856},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.7409992218017578},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5952659845352173},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5932143926620483},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5305604934692383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48555323481559753},{"id":"https://openalex.org/keywords/integrally-closed","display_name":"Integrally closed","score":0.46734076738357544},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.46163058280944824},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.43962469696998596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4254821538925171},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.42040252685546875},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4147099554538727},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3897939920425415},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3884381353855133}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9067509770393372},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8645774126052856},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7409992218017578},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5952659845352173},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5932143926620483},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5305604934692383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48555323481559753},{"id":"https://openalex.org/C205059728","wikidata":"https://www.wikidata.org/wiki/Q6042740","display_name":"Integrally closed","level":2,"score":0.46734076738357544},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.46163058280944824},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.43962469696998596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4254821538925171},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.42040252685546875},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4147099554538727},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3897939920425415},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3884381353855133},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005184","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005184","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322733","display_name":"Ministerstwo Edukacji i Nauki","ror":"https://ror.org/05dwvd537"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W382720801","https://openalex.org/W604307686","https://openalex.org/W1503971394","https://openalex.org/W1519801683","https://openalex.org/W1883676799","https://openalex.org/W1997243263","https://openalex.org/W2001235998","https://openalex.org/W2001596990","https://openalex.org/W2081659888","https://openalex.org/W2085919959","https://openalex.org/W2090149729","https://openalex.org/W2095956808","https://openalex.org/W2099697576","https://openalex.org/W2103643942","https://openalex.org/W2118905382","https://openalex.org/W2963540584","https://openalex.org/W3039948875"],"related_works":["https://openalex.org/W2386248435","https://openalex.org/W4212828952","https://openalex.org/W2762094349","https://openalex.org/W2033701980","https://openalex.org/W2963805867","https://openalex.org/W4367000290","https://openalex.org/W2892268807","https://openalex.org/W262066018","https://openalex.org/W1965853409","https://openalex.org/W2361990078"],"abstract_inverted_index":{"Let":[0],"A":[1,15,43,71,91],"be":[2],"a":[3,9,13,28],"finitely":[4],"generated":[5],"commutative":[6],"algebra":[7,48],"over":[8],"field":[10],"K":[11,17],"with":[12],"presentation":[14],"=":[16,44,53],"\u3008X":[18,54],"1":[19,37,55],",\u2026,":[20,38,56],"X":[21,36,39,57],"n":[22,40,58],"|":[23,59],"R\u3009,":[24],"where":[25],"R":[26,78],"is":[27,72,92],"set":[29],"of":[30,49,66,88],"monomial":[31],"relations":[32],"in":[33,64],"the":[34,46,50,67,85],"generators":[35],".":[41],"So":[42],"K[S],":[45],"semigroup":[47],"monoid":[51],"S":[52],"R\u3009.":[60],"We":[61],"characterize,":[62],"purely":[63],"terms":[65],"defining":[68],"relations,":[69],"when":[70],"an":[73],"integrally":[74],"closed":[75],"domain,":[76],"provided":[77],"contains":[79],"at":[80],"most":[81],"two":[82],"relations.":[83],"Also":[84],"class":[86],"group":[87],"such":[89],"algebras":[90],"calculated.":[93]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}