{"id":"https://openalex.org/W2140565804","doi":"https://doi.org/10.1142/s0218196708004858","title":"FREE REPRESENTABLE IDEMPOTENT COMMUTATIVE RESIDUATED LATTICES","display_name":"FREE REPRESENTABLE IDEMPOTENT COMMUTATIVE RESIDUATED LATTICES","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2140565804","doi":"https://doi.org/10.1142/s0218196708004858","mag":"2140565804"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004858","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004858","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/A5019482870","display_name":"Jeffrey S. Olson","orcid":null},"institutions":[{"id":"https://openalex.org/I169768744","display_name":"Norwich University","ror":"https://ror.org/04we7d902","country_code":"US","type":"education","lineage":["https://openalex.org/I169768744"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JEFFREY S. OLSON","raw_affiliation_strings":["Department of Mathematics, Norwich University, 158 Harmon Dr., Northfield, VT 05663, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Norwich University, 158 Harmon Dr., Northfield, VT 05663, USA","institution_ids":["https://openalex.org/I169768744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019482870"],"corresponding_institution_ids":["https://openalex.org/I169768744"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.14814437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"08","first_page":"1365","last_page":"1394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9067310690879822},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.8178063631057739},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.7259236574172974},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.68436598777771},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6177412271499634},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6011255383491516},{"id":"https://openalex.org/keywords/free-product","display_name":"Free product","score":0.570012092590332},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5660243630409241},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.351495623588562},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.06373390555381775}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9067310690879822},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.8178063631057739},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.7259236574172974},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.68436598777771},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6177412271499634},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6011255383491516},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.570012092590332},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5660243630409241},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.351495623588562},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.06373390555381775},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196708004858","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004858","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1503075583","https://openalex.org/W1965682580","https://openalex.org/W1984616877","https://openalex.org/W1986245444","https://openalex.org/W1989031758","https://openalex.org/W2040432965","https://openalex.org/W2057821078","https://openalex.org/W2077675813","https://openalex.org/W2156760583","https://openalex.org/W2317103523","https://openalex.org/W2914659449","https://openalex.org/W3047122219","https://openalex.org/W3159824982","https://openalex.org/W4285719527","https://openalex.org/W4318832420"],"related_works":["https://openalex.org/W4237107081","https://openalex.org/W3105245946","https://openalex.org/W2024371017","https://openalex.org/W2205307454","https://openalex.org/W2951659195","https://openalex.org/W168585031","https://openalex.org/W2001570562","https://openalex.org/W4386468199","https://openalex.org/W2862035520","https://openalex.org/W2963524535"],"abstract_inverted_index":{"The":[0],"structure":[1,29],"of":[2,8,12,30,50],"simple":[3],"and":[4,28,41],"directly":[5],"indecomposable":[6],"members":[7],"the":[9,26,39,47],"variety":[10],"RICRL":[11,51],"representable":[13],"idempotent":[14],"commutative":[15],"residuated":[16],"lattices":[17],"is":[18,52],"described.":[19],"These":[20],"descriptions":[21],"are":[22],"employed":[23],"to":[24],"determine":[25],"size":[27],"free":[31,48],"algebras":[32],"in":[33],"RICRL,":[34],"using":[35],"existing":[36],"theory":[37],"on":[38],"Fraser\u2013Horn":[40],"Apple":[42],"properties.":[43],"A":[44],"formula":[45],"for":[46],"spectrum":[49],"given.":[53]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
