{"id":"https://openalex.org/W4414523788","doi":"https://doi.org/10.3390/sym17101596","title":"A Note on Nonlinear Mappings Preserving the Bi-Skew Jordan-Type Product on Factor von Neumann Algebras","display_name":"A Note on Nonlinear Mappings Preserving the Bi-Skew Jordan-Type Product on Factor von Neumann Algebras","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414523788","doi":"https://doi.org/10.3390/sym17101596"},"language":"en","primary_location":{"id":"doi:10.3390/sym17101596","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101596","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1596/pdf?version=1758765367","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/10/1596/pdf?version=1758765367","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119734380","display_name":"Majed Almubark","orcid":null},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Majed Almubark","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100726233","display_name":"Asma Ali","orcid":"https://orcid.org/0000-0001-7602-0268"},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Asma Ali","raw_affiliation_strings":["Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","institution_ids":["https://openalex.org/I171210897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5118120311","display_name":"Tooba Naz","orcid":"https://orcid.org/0009-0006-7937-5180"},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Tooba Naz","raw_affiliation_strings":["Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","institution_ids":["https://openalex.org/I171210897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039380115","display_name":"Junaid Nisar","orcid":"https://orcid.org/0000-0001-9322-924X"},"institutions":[{"id":"https://openalex.org/I244572783","display_name":"Symbiosis International University","ror":"https://ror.org/005r2ww51","country_code":"IN","type":"education","lineage":["https://openalex.org/I244572783"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Junaid Nisar","raw_affiliation_strings":["Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune 412115, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune 412115, India","institution_ids":["https://openalex.org/I244572783"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5118120311"],"corresponding_institution_ids":["https://openalex.org/I171210897"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32111819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"10","first_page":"1596","last_page":"1596"},"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":0.9968000054359436,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9925000071525574,"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/bijection","display_name":"Bijection","score":0.9280999898910522},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.7763000130653381},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.5803999900817871},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5741999745368958},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5171999931335449},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.48989999294281006},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9280999898910522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8033999800682068},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7763000130653381},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.5803999900817871},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5741999745368958},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5171999931335449},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47859999537467957},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4399999976158142},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C144133476","wikidata":"https://www.wikidata.org/wiki/Q4666687","display_name":"Abelian von Neumann algebra","level":5,"score":0.39160001277923584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36899998784065247},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.3587000072002411},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32739999890327454},{"id":"https://openalex.org/C153408630","wikidata":"https://www.wikidata.org/wiki/Q1970172","display_name":"Von Neumann algebra","level":3,"score":0.3248000144958496},{"id":"https://openalex.org/C21261745","wikidata":"https://www.wikidata.org/wiki/Q7941491","display_name":"Von Neumann's theorem","level":4,"score":0.29589998722076416},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17101596","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101596","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1596/pdf?version=1758765367","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"}],"best_oa_location":{"id":"doi:10.3390/sym17101596","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101596","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1596/pdf?version=1758765367","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":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414523788.pdf","grobid_xml":"https://content.openalex.org/works/W4414523788.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W75654438","https://openalex.org/W1964310052","https://openalex.org/W2016757429","https://openalex.org/W2042338298","https://openalex.org/W2075915751","https://openalex.org/W2078582861","https://openalex.org/W2154659791","https://openalex.org/W2276014232","https://openalex.org/W2317667104","https://openalex.org/W2460748524","https://openalex.org/W2511243136","https://openalex.org/W2614805061","https://openalex.org/W2767307911","https://openalex.org/W2998026225","https://openalex.org/W3138390543","https://openalex.org/W4290973953","https://openalex.org/W4411193767"],"related_works":[],"abstract_inverted_index":{"Let":[0],"E":[1,12,37],"and":[2,20,38,58,83,91],"F":[3,39],"be":[4],"two":[5],"factor":[6],"von":[7],"Neumann":[8],"algebras":[9],"such":[10],"that":[11,67],"contains":[13],"a":[14,32,61,72,77],"nontrivial":[15],"symmetric":[16],"idempotent":[17],"element":[18,23],"e":[19],"an":[21],"identity":[22],"I,":[24],"with":[25],"dim(E)\u22652.":[26],"In":[27,93],"this":[28,94],"article,":[29],"we":[30,96],"consider":[31],"bijective":[33,99],"map":[34],"\u03d1":[35,68],"between":[36],"satisfying":[40],"\u03d1(\u03bd1\u2605\u03bd2\u2605\u03bd3\u2605\u22ef\u2605\u03bdn)=\u03d1(\u03bd1)\u2605\u03d1(\u03bd2)\u2605\u03d1(\u03bd3)\u2605\u22ef\u2605\u03d1(\u03bdn)":[41],"for":[42,55,81,104],"all":[43],"\u03bdi\u2208E(i=1,2,\u2026,n),":[44],"where":[45],"\u03bdi\u2605\u03bdj=\u03bdi\u2217\u03bdj+\u03bdj\u2217\u03bdi":[46],"is":[47,60,71,110],"the":[48,102],"bi-skew":[49],"Jordan":[50],"product":[51],"of":[52,115],"\u03bdi,":[53],"\u03bdj":[54],"any":[56,105],"1\u2264i,j\u2264n,":[57],"n\u22652":[59],"fixed":[62],"positive":[63],"integer.":[64],"We":[65],"prove":[66],"or":[69,76],"\u2212\u03d1":[70],"conjugate":[73],"linear":[74,78],"\u2217-isomorphism":[75],"\u2217-isomorphism.":[79],"Moreover,":[80],"n=2":[82],"n=3,":[84],"similar":[85],"results":[86],"were":[87],"obtained":[88],"by":[89],"Li":[90],"Zhang.":[92],"work,":[95],"characterize":[97],"nonlinear":[98],"maps":[100],"preserving":[101],"n-product":[103],"n\u22652.":[106],"Thus,":[107],"our":[108],"result":[109],"more":[111],"general":[112],"than":[113],"both":[114],"these":[116],"earlier":[117],"results.":[118]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
