{"id":"https://openalex.org/W2886100083","doi":"https://doi.org/10.3390/sym10080322","title":"A Historical Perspective of the Theory of Isotopisms","display_name":"A Historical Perspective of the Theory of Isotopisms","publication_year":2018,"publication_date":"2018-08-03","ids":{"openalex":"https://openalex.org/W2886100083","doi":"https://doi.org/10.3390/sym10080322","mag":"2886100083"},"language":"en","primary_location":{"id":"doi:10.3390/sym10080322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080322","pdf_url":"https://www.mdpi.com/2073-8994/10/8/322/pdf?version=1533301908","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/8/322/pdf?version=1533301908","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012079186","display_name":"Ra\u00fal Manuel Falc\u00f3n Ganfornina","orcid":"https://orcid.org/0000-0002-6474-7301"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ra\u00fal M. Falc\u00f3n","raw_affiliation_strings":["Department Applied Mathematics I, University of Sevilla, 41004 Seville, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6474-7301","affiliations":[{"raw_affiliation_string":"Department Applied Mathematics I, University of Sevilla, 41004 Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027380669","display_name":"\u00d3scar J. Falc\u00f3n","orcid":"https://orcid.org/0000-0001-6658-3454"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"\u00d3scar J. Falc\u00f3n","raw_affiliation_strings":["Department Geometry and Topology, University of Sevilla, 41004 Seville, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Geometry and Topology, University of Sevilla, 41004 Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064904109","display_name":"Juan N\u00fa\u00f1ez Vald\u00e9s","orcid":"https://orcid.org/0000-0002-8413-6735"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan N\u00fa\u00f1ez","raw_affiliation_strings":["Department Geometry and Topology, University of Sevilla, 41004 Seville, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Geometry and Topology, University of Sevilla, 41004 Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012079186"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.2855,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8773503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"8","first_page":"322","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.98089998960495,"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/generalization","display_name":"Generalization","score":0.714358389377594},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6974630355834961},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5170662999153137},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.502213716506958},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5013256072998047},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4778137505054474},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4486531913280487},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4468315541744232},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42757153511047363},{"id":"https://openalex.org/keywords/development","display_name":"Development (topology)","score":0.41930633783340454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41083085536956787},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.34302425384521484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3385382890701294},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18299919366836548},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.10831788182258606}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.714358389377594},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6974630355834961},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5170662999153137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.502213716506958},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5013256072998047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4778137505054474},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4486531913280487},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4468315541744232},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42757153511047363},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.41930633783340454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41083085536956787},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.34302425384521484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3385382890701294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18299919366836548},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.10831788182258606},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym10080322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080322","pdf_url":"https://www.mdpi.com/2073-8994/10/8/322/pdf?version=1533301908","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:idus.us.es:11441/78584","is_oa":false,"landing_page_url":"https://idus.us.es/handle//11441/78584","pdf_url":null,"source":{"id":"https://openalex.org/S4306400333","display_name":"idUS (Universidad de Sevilla)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79238269","host_organization_name":"Universidad de Sevilla","host_organization_lineage":["https://openalex.org/I79238269"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e76270b044564c1caeda01010630686a","is_oa":true,"landing_page_url":"https://doaj.org/article/e76270b044564c1caeda01010630686a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 10, Iss 8, p 322 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/8/322/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10080322","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym10080322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080322","pdf_url":"https://www.mdpi.com/2073-8994/10/8/322/pdf?version=1533301908","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2886100083.pdf"},"referenced_works_count":160,"referenced_works":["https://openalex.org/W87392048","https://openalex.org/W124080408","https://openalex.org/W153077712","https://openalex.org/W165183415","https://openalex.org/W642601980","https://openalex.org/W658262679","https://openalex.org/W935598545","https://openalex.org/W1500381180","https://openalex.org/W1543193062","https://openalex.org/W1570999794","https://openalex.org/W1677135960","https://openalex.org/W1825715517","https://openalex.org/W1857252114","https://openalex.org/W1899294640","https://openalex.org/W1908044368","https://openalex.org/W1911411026","https://openalex.org/W1963652265","https://openalex.org/W1963741548","https://openalex.org/W1964285115","https://openalex.org/W1965020049","https://openalex.org/W1965237675","https://openalex.org/W1965459688","https://openalex.org/W1966607921","https://openalex.org/W1972264470","https://openalex.org/W1974290399","https://openalex.org/W1974487335","https://openalex.org/W1976434884","https://openalex.org/W1977463864","https://openalex.org/W1979860197","https://openalex.org/W1980498468","https://openalex.org/W1982352694","https://openalex.org/W1988765753","https://openalex.org/W1989673299","https://openalex.org/W1992245930","https://openalex.org/W1992369703","https://openalex.org/W1992701020","https://openalex.org/W1994650277","https://openalex.org/W1994793218","https://openalex.org/W1997290697","https://openalex.org/W1998520828","https://openalex.org/W1998921562","https://openalex.org/W1999179925","https://openalex.org/W1999680025","https://openalex.org/W2001834993","https://openalex.org/W2004639356","https://openalex.org/W2005986500","https://openalex.org/W2008689074","https://openalex.org/W2009508707","https://openalex.org/W2009510707","https://openalex.org/W2015465448","https://openalex.org/W2015751597","https://openalex.org/W2017187965","https://openalex.org/W2018187768","https://openalex.org/W2018931517","https://openalex.org/W2020332469","https://openalex.org/W2021886305","https://openalex.org/W2022821512","https://openalex.org/W2023167266","https://openalex.org/W2024088248","https://openalex.org/W2024991606","https://openalex.org/W2025249653","https://openalex.org/W2025258516","https://openalex.org/W2025927713","https://openalex.org/W2026024802","https://openalex.org/W2028503775","https://openalex.org/W2033627833","https://openalex.org/W2036243090","https://openalex.org/W2036780368","https://openalex.org/W2040253880","https://openalex.org/W2040493278","https://openalex.org/W2042619813","https://openalex.org/W2045411730","https://openalex.org/W2050213288","https://openalex.org/W2052901422","https://openalex.org/W2053838289","https://openalex.org/W2057552658","https://openalex.org/W2063408493","https://openalex.org/W2063463511","https://openalex.org/W2065290556","https://openalex.org/W2067284818","https://openalex.org/W2073054884","https://openalex.org/W2073336963","https://openalex.org/W2073936290","https://openalex.org/W2074081326","https://openalex.org/W2074629400","https://openalex.org/W2079838836","https://openalex.org/W2080292295","https://openalex.org/W2081836846","https://openalex.org/W2082717330","https://openalex.org/W2083617777","https://openalex.org/W2083844543","https://openalex.org/W2085178750","https://openalex.org/W2087406041","https://openalex.org/W2090504196","https://openalex.org/W2091148878","https://openalex.org/W2093445952","https://openalex.org/W2093750171","https://openalex.org/W2094774006","https://openalex.org/W2095429194","https://openalex.org/W2112641412","https://openalex.org/W2133516196","https://openalex.org/W2145524137","https://openalex.org/W2152951761","https://openalex.org/W2154750111","https://openalex.org/W2224278053","https://openalex.org/W2230823414","https://openalex.org/W2252843702","https://openalex.org/W2313586032","https://openalex.org/W2313696386","https://openalex.org/W2315523759","https://openalex.org/W2319797207","https://openalex.org/W2323810788","https://openalex.org/W2326906329","https://openalex.org/W2333917077","https://openalex.org/W2335771728","https://openalex.org/W2338054667","https://openalex.org/W2467726098","https://openalex.org/W2502324810","https://openalex.org/W2526425885","https://openalex.org/W2586187096","https://openalex.org/W2601649413","https://openalex.org/W2604933633","https://openalex.org/W2610502221","https://openalex.org/W2611980197","https://openalex.org/W2752153945","https://openalex.org/W2808757355","https://openalex.org/W2883063504","https://openalex.org/W2884099099","https://openalex.org/W2911683105","https://openalex.org/W2963265631","https://openalex.org/W2963931126","https://openalex.org/W2964107006","https://openalex.org/W2964344819","https://openalex.org/W3029265087","https://openalex.org/W3105633767","https://openalex.org/W3121375286","https://openalex.org/W3141604666","https://openalex.org/W3184969723","https://openalex.org/W3197004285","https://openalex.org/W4229875880","https://openalex.org/W4231847244","https://openalex.org/W4234230816","https://openalex.org/W4237207618","https://openalex.org/W4238074878","https://openalex.org/W4238841606","https://openalex.org/W4240075532","https://openalex.org/W4244525298","https://openalex.org/W4246088357","https://openalex.org/W4253109386","https://openalex.org/W4362174647","https://openalex.org/W6606219174","https://openalex.org/W6617859817","https://openalex.org/W6640266095","https://openalex.org/W6691621105","https://openalex.org/W6692888311","https://openalex.org/W6741643510","https://openalex.org/W6743907819","https://openalex.org/W6823327580","https://openalex.org/W6983385526","https://openalex.org/W7017635788"],"related_works":["https://openalex.org/W4300711749","https://openalex.org/W3162204513","https://openalex.org/W2246967737","https://openalex.org/W2371138613","https://openalex.org/W2080482296","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W1492794944","https://openalex.org/W2239445980"],"abstract_inverted_index":{"In":[0,70],"the":[1,4,11,24,52,55,82],"middle":[2],"of":[3,13,15,23,27,47,59,72,86],"twentieth":[5],"century,":[6],"Albert":[7],"and":[8,18,33,57,62,84],"Bruck":[9],"introduced":[10],"theory":[12,26],"isotopisms":[14],"non-associative":[16],"algebras":[17],"quasigroups":[19],"as":[20],"a":[21,44,88,93],"generalization":[22],"classical":[25],"isomorphisms":[28],"in":[29,51,96],"order":[30],"to":[31,38,66],"study":[32],"classify":[34],"such":[35,87],"structures":[36,64],"according":[37,65],"more":[39],"general":[40],"symmetries.":[41],"Since":[42],"then,":[43],"wide":[45],"range":[46],"applications":[48],"have":[49],"arisen":[50],"literature":[53],"concerning":[54],"classification":[56],"enumeration":[58],"different":[60],"algebraic":[61],"combinatorial":[63],"their":[67],"isotopism":[68],"classes.":[69],"spite":[71],"that,":[73],"there":[74],"does":[75],"not":[76],"exist":[77],"any":[78],"contribution":[79],"dealing":[80],"with":[81],"origin":[83],"development":[85],"theory.":[89],"This":[90],"paper":[91],"is":[92],"first":[94],"approach":[95],"this":[97],"regard.":[98]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2018-08-22T00:00:00"}