{"id":"https://openalex.org/W2007031430","doi":"https://doi.org/10.1134/s0361768809020042","title":"Role of involutive criteria in computing Boolean Gr\u00f6bner bases","display_name":"Role of involutive criteria in computing Boolean Gr\u00f6bner bases","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2007031430","doi":"https://doi.org/10.1134/s0361768809020042","mag":"2007031430"},"language":"en","primary_location":{"id":"doi:10.1134/s0361768809020042","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0361768809020042","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261","3034-5847"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","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/A5065468649","display_name":"Vladimir P. Gerdt","orcid":"https://orcid.org/0000-0002-0825-1811"},"institutions":[{"id":"https://openalex.org/I32699454","display_name":"Joint Institute for Nuclear Research","ror":"https://ror.org/044yd9t77","country_code":"RU","type":"facility","lineage":["https://openalex.org/I32699454"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"V. P. Gerdt","raw_affiliation_strings":["Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia","Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia","Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980","institution_ids":["https://openalex.org/I32699454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074794408","display_name":"M. V. Zinin","orcid":null},"institutions":[{"id":"https://openalex.org/I32699454","display_name":"Joint Institute for Nuclear Research","ror":"https://ror.org/044yd9t77","country_code":"RU","type":"facility","lineage":["https://openalex.org/I32699454"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"M. V. Zinin","raw_affiliation_strings":["Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia","Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia","Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980","institution_ids":["https://openalex.org/I32699454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065468649"],"corresponding_institution_ids":["https://openalex.org/I32699454"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09187645,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"2","first_page":"90","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9965000152587891,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-ring","display_name":"Boolean ring","score":0.623328685760498},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6067701578140259},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5977945327758789},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5509490370750427},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5394770503044128},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5392166376113892},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.4507850408554077},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.43123024702072144},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42643752694129944},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41274186968803406},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.2722185254096985},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.2568047046661377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21179628372192383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1632256805896759},{"id":"https://openalex.org/keywords/quotient-ring","display_name":"Quotient ring","score":0.042471468448638916}],"concepts":[{"id":"https://openalex.org/C128134353","wikidata":"https://www.wikidata.org/wiki/Q2634401","display_name":"Boolean ring","level":5,"score":0.623328685760498},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6067701578140259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5977945327758789},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5509490370750427},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5394770503044128},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5392166376113892},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.4507850408554077},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.43123024702072144},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42643752694129944},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41274186968803406},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2722185254096985},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.2568047046661377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21179628372192383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1632256805896759},{"id":"https://openalex.org/C19787925","wikidata":"https://www.wikidata.org/wiki/Q619436","display_name":"Quotient ring","level":4,"score":0.042471468448638916},{"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/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},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1134/s0361768809020042","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0361768809020042","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261","3034-5847"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","raw_type":"journal-article"},{"id":"pmh:oai:jdsweb.jinr.ru:921","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/S0361768809020042","pdf_url":null,"source":{"id":"https://openalex.org/S4306401136","display_name":"High-Energy Physics Literature Database (CERN, DESY, Fermilab, IHEP, and SLAC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W156666843","https://openalex.org/W1510162831","https://openalex.org/W1518341038","https://openalex.org/W1543638401","https://openalex.org/W1790316935","https://openalex.org/W2038345254","https://openalex.org/W2051046060","https://openalex.org/W2060036014","https://openalex.org/W2077725083","https://openalex.org/W2080868322","https://openalex.org/W2083251752","https://openalex.org/W2090397743","https://openalex.org/W2093299949","https://openalex.org/W2099172492","https://openalex.org/W2128687423","https://openalex.org/W2137378957","https://openalex.org/W2319466955","https://openalex.org/W2561675875","https://openalex.org/W2591842745","https://openalex.org/W2995200218","https://openalex.org/W3039948875","https://openalex.org/W3043060850","https://openalex.org/W4238858352","https://openalex.org/W6776623540"],"related_works":["https://openalex.org/W2740171735","https://openalex.org/W2940617399","https://openalex.org/W3202105211","https://openalex.org/W2330826321","https://openalex.org/W2145243037","https://openalex.org/W4255990987","https://openalex.org/W4247342663","https://openalex.org/W2111089041","https://openalex.org/W79842022","https://openalex.org/W1988612506"],"abstract_inverted_index":{"In":[0],"this":[1,30,67],"paper,":[2],"effectiveness":[3],"of":[4,19,26,29,38,57,62,66,73,83],"using":[5],"four":[6],"criteria":[7,40,78],"in":[8,41,43,51,53],"an":[9,54],"involutive":[10],"algorithm":[11],"based":[12],"on":[13],"the":[14,27,33,36,39,60,71,74,84],"Pommaret":[15],"division":[16],"for":[17],"construction":[18],"Boolean":[20,44],"Gr\u00f6bner":[21],"bases":[22],"is":[23,32,46,69,79],"studied.":[24],"One":[25],"results":[28],"study":[31,68],"observation":[34],"that":[35,50,70,82],"role":[37],"computations":[42,52],"rings":[45],"much":[47],"less":[48],"than":[49,81],"ordinary":[55],"ring":[56],"polynomials":[58],"over":[59],"field":[61],"integers.":[63],"Another":[64],"conclusion":[65],"efficiency":[72],"second":[75],"and/or":[76],"third":[77],"higher":[80],"two":[85],"others.":[86]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
