{"id":"https://openalex.org/W1985758118","doi":"https://doi.org/10.1142/s0218196798000090","title":"Derived Varieties and Derived Equational Theories","display_name":"Derived Varieties and Derived Equational Theories","publication_year":1998,"publication_date":"1998-04-01","ids":{"openalex":"https://openalex.org/W1985758118","doi":"https://doi.org/10.1142/s0218196798000090","mag":"1985758118"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196798000090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000090","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/A5055124509","display_name":"Klaus Denecke","orcid":"https://orcid.org/0000-0003-4882-0449"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"K. Denecke","raw_affiliation_strings":["University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany"],"affiliations":[{"raw_affiliation_string":"University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070193335","display_name":"J\u00f6rg Koppitz","orcid":"https://orcid.org/0000-0002-1687-4656"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. Koppitz","raw_affiliation_strings":["University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany"],"affiliations":[{"raw_affiliation_string":"University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064603688","display_name":"Roman Marsza\u0142ek","orcid":null},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]},{"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":"R. Marsza\u0142ek","raw_affiliation_strings":["University of Wroc\u0142aw, Institute of Mathematics, pl. Grunwaldzki 2/4 Wroc\u0142aw, Poland"],"affiliations":[{"raw_affiliation_string":"University of Wroc\u0142aw, Institute of Mathematics, pl. Grunwaldzki 2/4 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055124509"],"corresponding_institution_ids":["https://openalex.org/I176453806"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11006969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"08","issue":"02","first_page":"153","last_page":"169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8274000287055969,"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":0.8274000287055969,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.7253000140190125,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.7228999733924866,"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":0.8502289056777954},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.7938027381896973},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.657072901725769},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6344572901725769},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.581158459186554},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5186145305633545},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.51618891954422},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5145239233970642},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.5076643228530884},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49106407165527344},{"id":"https://openalex.org/keywords/universal-algebra","display_name":"Universal algebra","score":0.4590325653553009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07719415426254272}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8502289056777954},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.7938027381896973},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.657072901725769},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6344572901725769},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.581158459186554},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5186145305633545},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.51618891954422},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5145239233970642},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.5076643228530884},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49106407165527344},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.4590325653553009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07719415426254272},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196798000090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000090","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"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:23349","is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/23349","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2010369003","https://openalex.org/W2031540104","https://openalex.org/W2032962859"],"related_works":["https://openalex.org/W2560853036","https://openalex.org/W2566696415","https://openalex.org/W1563787543","https://openalex.org/W2909241626","https://openalex.org/W2890304493","https://openalex.org/W2966241533","https://openalex.org/W590015412","https://openalex.org/W4211144708","https://openalex.org/W4211021113","https://openalex.org/W4234828150"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,25,61,71,129,132,138],"derivation":[4,139,146],"process":[5],"for":[6,148],"varieties":[7,114,127],"and":[8,16,115],"equational":[9,117],"theories":[10,118],"using":[11],"the":[12,34,54,82,89,98,102,110,122,142,145,149],"theory":[13],"of":[14,21,33,40,50,64,73,75,91,112,124,128,153],"hypersubstitutions":[15],"M-hyperidentities.":[17],"A":[18],"hypersubstitution":[19],"\u03c3":[20,85],"type":[22,35,51,76],"\u03c4":[23,52,77],"is":[24,47,59,70,134,156],"map":[26],"which":[27,136],"takes":[28],"each":[29],"n-ary":[30,38],"operation":[31],"symbol":[32],"to":[36],"an":[37,48],"term":[39],"this":[41],"type.":[42],"If":[43,68],"[Formula:":[44,56,65],"see":[45,57,66],"text]":[46,58],"algebra":[49,55,63],"then":[53,78],"called":[60],"derived":[62,93,113,116,126],"text].":[67],"V":[69],"class":[72,90],"algebras":[74,94],"one":[79],"can":[80],"consider":[81],"variety":[83,152],"v":[84],"(V)":[86],"generated":[87],"by":[88],"all":[92,125],"from":[95],"V.":[96],"In":[97,107,141],"first":[99],"two":[100],"sections":[101],"necessary":[103],"definitions":[104],"are":[105,119],"given.":[106],"Sec.":[108],"3":[109],"properties":[111],"described.":[120],"On":[121],"set":[123],"given":[130],"variety,":[131],"quasiorder":[133],"developed":[135],"gives":[137],"diagram.":[140],"final":[143],"section":[144],"diagram":[147],"largest":[150],"solid":[151],"medial":[154],"semigroups":[155],"worked":[157],"out.":[158]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}