{"id":"https://openalex.org/W2808961372","doi":"https://doi.org/10.1142/s0218196718500443","title":"The equation solvability problem over supernilpotent algebras with Mal\u2019cev term","display_name":"The equation solvability problem over supernilpotent algebras with Mal\u2019cev term","publication_year":2018,"publication_date":"2018-06-18","ids":{"openalex":"https://openalex.org/W2808961372","doi":"https://doi.org/10.1142/s0218196718500443","mag":"2808961372"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500443","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500443","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/A5063365809","display_name":"Michael Kompatscher","orcid":"https://orcid.org/0000-0002-0163-6604"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Kompatscher","raw_affiliation_strings":["Department of Algebra, MFF UK, Sokolovska 83, 186 00 Praha 8, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, MFF UK, Sokolovska 83, 186 00 Praha 8, Czech Republic","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063365809"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0097,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.78345799,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"06","first_page":"1005","last_page":"1015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987999796867371,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9987999796867371,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9976000189781189,"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":0.8974202275276184},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.7493095397949219},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7442924380302429},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5175777673721313},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5175592303276062},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5064073801040649},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4204385578632355},{"id":"https://openalex.org/keywords/nilpotent-group","display_name":"Nilpotent group","score":0.4164227843284607}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8974202275276184},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7493095397949219},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7442924380302429},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5175777673721313},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5175592303276062},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5064073801040649},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4204385578632355},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.4164227843284607},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196718500443","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500443","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/F4320309755","display_name":"Univerzita Karlova v Praze","ror":"https://ror.org/024d6js02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1971935730","https://openalex.org/W1975052726","https://openalex.org/W1999377233","https://openalex.org/W2002247104","https://openalex.org/W2006336761","https://openalex.org/W2084284300","https://openalex.org/W2092435018","https://openalex.org/W2109957355","https://openalex.org/W2127525529","https://openalex.org/W2136969434","https://openalex.org/W2766348174","https://openalex.org/W2963657431"],"related_works":["https://openalex.org/W2022486451","https://openalex.org/W2153554103","https://openalex.org/W3184171495","https://openalex.org/W2359607255","https://openalex.org/W3171737361","https://openalex.org/W2118240797","https://openalex.org/W2951885157","https://openalex.org/W2055652047","https://openalex.org/W3214836282","https://openalex.org/W4298849012"],"abstract_inverted_index":{"In":[0,21],"2011,":[1],"Horv\u00e1th":[2],"gave":[3],"a":[4,50,57],"new":[5],"proof":[6,29],"that":[7,40,68,81],"the":[8,22,82],"equation":[9,76],"solvability":[10,77],"problem":[11],"over":[12],"finite":[13],"nilpotent":[14,34],"groups":[15],"and":[16,74],"rings":[17],"is":[18,42,87],"in":[19,36,43,89],"P.":[20],"same":[23],"paper,":[24],"he":[25],"asked":[26],"whether":[27],"his":[28],"can":[30],"be":[31],"lifted":[32],"to":[33,84],"algebras":[35,48,64],"general.":[37],"We":[38],"show":[39],"this":[41],"fact":[44],"possible":[45],"for":[46],"supernilpotent":[47,63],"with":[49,65],"Mal\u2019cev":[51,66],"term.":[52],"However,":[53],"we":[54],"also":[55],"describe":[56],"class":[58],"of":[59],"nilpotent,":[60],"but":[61],"not":[62],"term":[67],"have":[69],"co-NP-complete":[70],"identity":[71],"checking":[72],"problems":[73],"NP-complete":[75],"problems.":[78],"This":[79],"proves":[80],"answer":[83],"Horv\u00e1th\u2019s":[85],"question":[86],"negative":[88],"general":[90],"(assuming":[91],"P[Formula:":[92],"see":[93],"text]NP).":[94]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}