{"id":"https://openalex.org/W3162427515","doi":"https://doi.org/10.1142/s0218196721500326","title":"Orthogonality graphs of real Cayley\u2013Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons","display_name":"Orthogonality graphs of real Cayley\u2013Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons","publication_year":2021,"publication_date":"2021-05-05","ids":{"openalex":"https://openalex.org/W3162427515","doi":"https://doi.org/10.1142/s0218196721500326","mag":"3162427515"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721500326","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500326","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/A5083799000","display_name":"Svetlana Zhilina","orcid":"https://orcid.org/0000-0002-0447-7274"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]},{"id":"https://openalex.org/I4210092319","display_name":"Moscow Center For Continuous Mathematical Education","ror":"https://ror.org/00dhbnv07","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210092319"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Svetlana Zhilina","raw_affiliation_strings":["Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow 119991, Russia","Moscow Center for Fundamental and Applied Mathematics, Moscow 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Moscow Center for Fundamental and Applied Mathematics, Moscow 119991, Russia","institution_ids":["https://openalex.org/I4210092319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083799000"],"corresponding_institution_ids":["https://openalex.org/I19880235","https://openalex.org/I4210092319"],"apc_list":null,"apc_paid":null,"fwci":1.3207,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77772104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"04","first_page":"663","last_page":"689"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T14286","display_name":"Parkinson's Disease and Spinal Disorders","score":0.9059000015258789,"subfield":{"id":"https://openalex.org/subfields/2728","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.901199996471405,"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":0.9068365693092346},{"id":"https://openalex.org/keywords/zero-divisor","display_name":"Zero divisor","score":0.8189834952354431},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.5582051873207092},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5558235049247742},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46626362204551697},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44519761204719543},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.44348156452178955},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.4178473949432373},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4164350628852844},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38817334175109863},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34000930190086365}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9068365693092346},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.8189834952354431},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.5582051873207092},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5558235049247742},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46626362204551697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44519761204719543},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.44348156452178955},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.4178473949432373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4164350628852844},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38817334175109863},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34000930190086365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196721500326","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500326","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1504695943","https://openalex.org/W1989093153","https://openalex.org/W2077459879","https://openalex.org/W2331296818","https://openalex.org/W2754250893","https://openalex.org/W2911683105","https://openalex.org/W2955306551","https://openalex.org/W2964072513","https://openalex.org/W2964257931","https://openalex.org/W3045223973","https://openalex.org/W4235693166"],"related_works":["https://openalex.org/W2147421839","https://openalex.org/W2963575964","https://openalex.org/W2162054958","https://openalex.org/W2372618431","https://openalex.org/W2097947972","https://openalex.org/W2120359860","https://openalex.org/W3080370734","https://openalex.org/W3113897730","https://openalex.org/W2087357635","https://openalex.org/W1994058133"],"abstract_inverted_index":{"We":[0,52,99],"study":[1],"zero":[2,15,34,87],"divisors":[3,88],"whose":[4,89],"components":[5,90],"alternate":[6],"strongly":[7],"pairwise":[8],"and":[9,42,102,105],"construct":[10],"oriented":[11],"hexagons":[12],"in":[13],"the":[14,27,30,33,39,54,58],"divisor":[16,35],"graph":[17,36],"of":[18,26,29,57,60,78],"an":[19,75,79],"arbitrary":[20,80],"real":[21],"Cayley\u2013Dickson":[22,81],"algebra.":[23,82],"In":[24],"case":[25],"algebras":[28],"main":[31],"sequence,":[32],"coincides":[37],"with":[38],"orthogonality":[40],"graph,":[41],"any":[43],"hexagon":[44],"can":[45],"be":[46],"extended":[47],"to":[48,73,97],"a":[49,61,67],"double":[50,62],"hexagon.":[51,63],"determine":[53,103],"multiplication":[55],"table":[56],"vertices":[59],"Then":[64],"we":[65,84],"find":[66],"sufficient":[68,106],"condition":[69],"for":[70],"three":[71],"elements":[72,95,112],"generate":[74],"alternative":[76],"subalgebra":[77],"Finally,":[83],"consider":[85],"those":[86],"are":[91,113],"both":[92],"standard":[93],"basis":[94],"up":[96],"sign.":[98],"classify":[100],"them":[101],"necessary":[104],"conditions":[107],"under":[108],"which":[109],"two":[110],"such":[111],"orthogonal.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}