{"id":"https://openalex.org/W2037998074","doi":"https://doi.org/10.1155/2012/925092","title":"Zero Triple Product Determined Matrix Algebras","display_name":"Zero Triple Product Determined Matrix Algebras","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2037998074","doi":"https://doi.org/10.1155/2012/925092","mag":"2037998074"},"language":"en","primary_location":{"id":"doi:10.1155/2012/925092","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/925092","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/925092.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/925092.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101887539","display_name":"Hongmei Yao","orcid":"https://orcid.org/0000-0001-7772-8006"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongmei Yao","raw_affiliation_strings":["College of Science, Harbin Engineering University, Harbin 150001, China","Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Harbin Engineering University, Harbin 150001, China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102204108","display_name":"Baodong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baodong Zheng","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China","Department of Mathematics, Harbin Institute of Technology, Harbin  150001, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin  150001, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101887539"],"corresponding_institution_ids":["https://openalex.org/I151727225","https://openalex.org/I204983213"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.2922,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.86011711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9945999979972839,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.984000027179718,"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/algorithm","display_name":"Algorithm","score":0.5727379322052002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33433449268341064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2781776785850525}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5727379322052002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33433449268341064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2781776785850525}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/925092","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/925092","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/925092.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495056","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495056","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:925092","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/925092.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:8db532f682e741e3a1f4acd37bbd9fd4","is_oa":true,"landing_page_url":"https://doaj.org/article/8db532f682e741e3a1f4acd37bbd9fd4","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/925092","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/925092","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/925092.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1371202983","display_name":null,"funder_award_id":"HEUCF20111132","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3840195097","display_name":null,"funder_award_id":"10871056","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3906878917","display_name":null,"funder_award_id":"HEUCF20111132","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4869761776","display_name":null,"funder_award_id":"HEUCF","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8287229873","display_name":null,"funder_award_id":"10871056","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037998074.pdf","grobid_xml":"https://content.openalex.org/works/W2037998074.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1584041513","https://openalex.org/W2022471939","https://openalex.org/W2032193690","https://openalex.org/W2038218125","https://openalex.org/W2049687882","https://openalex.org/W2061617430","https://openalex.org/W2067772232","https://openalex.org/W2071887868","https://openalex.org/W2074591550","https://openalex.org/W2093544323","https://openalex.org/W2098561286","https://openalex.org/W2136169847","https://openalex.org/W3147141315"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Let":[0],"A":[1,15,62,90,108],"be":[2],"an":[3],"algebra":[4,122,137,146],"over":[5],"a":[6,56],"commutative":[7,135,144],"unital":[8,136,145],"ring":[9],"\ud835\udc9e":[10,24,57,147],".":[11,91],"We":[12],"say":[13],"that":[14,67,120],"is":[16,101,109,133,149,166,174],"zero":[17,111,151,176],"triple":[18,95,105,113,152,178],"product":[19,96,114,153,179],"determined":[20],"if":[21,37],"for":[22,82],"every":[23,28],"\u2010module":[25],"X":[26,65],"and":[27,155],"trilinear":[29],"map":[30],"{\u00b7,":[31],"\u00b7,":[32],"\u00b7},":[33],"the":[34,93,98,141],"following":[35],"holds:":[36],"{":[38,68],"x":[39,48,69,78,84],",":[40,42,70,72,85,87,148],"y":[41,49,71,79,86],"z":[43,50,73,80,88],"}":[44,74],"=":[45,51,75],"0":[46],"whenever":[47],"0,":[52],"then":[53,107],"there":[54],"exists":[55],"\u2010linear":[58],"operator":[59],"T":[60,76],":":[61],"3":[63],"\u2192":[64],"such":[66],"(":[77,125,158],")":[81],"all":[83],"\u2208":[89],"If":[92],"ordinary":[94],"in":[97],"aforementioned":[99],"definition":[100],"replaced":[102],"by":[103],"Jordan":[104,112,177],"product,":[106],"called":[110],"determined.":[115,180],"This":[116],"paper":[117],"mainly":[118],"shows":[119],"matrix":[121],"M":[123,156],"n":[124,128,157,161],"B":[126,132],"),":[127,160],"\u2265":[129,162],"3,":[130,163],"where":[131,164],"any":[134,167],"even":[138],"different":[139],"from":[140],"above":[142],"mentioned":[143],"always":[150],"determined,":[154],"F":[159,165,171],"field":[168],"with":[169],"ch":[170],"\u2260":[172],"2,":[173],"also":[175]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
