{"id":"https://openalex.org/W2997679552","doi":"https://doi.org/10.48550/arxiv.2001.00328","title":"Jacobson's Lemma for the generalized n-strongly Drazin inverse","display_name":"Jacobson's Lemma for the generalized n-strongly Drazin inverse","publication_year":2020,"publication_date":"2020-01-02","ids":{"openalex":"https://openalex.org/W2997679552","doi":"https://doi.org/10.48550/arxiv.2001.00328","mag":"2997679552"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2001.00328","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00328","pdf_url":"https://arxiv.org/pdf/2001.00328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.00328","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031015351","display_name":"Huanyin Chen","orcid":"https://orcid.org/0000-0001-8184-1327","observed_orcids":["https://orcid.org/0000-0001-8184-1327"]},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Huanyin","raw_affiliation_strings":["Department of Mathematics , Hangzhou Normal University , Hang -zhou , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hangzhou Normal University , Hang -zhou , China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043634685","display_name":"Marjan Sheibani","orcid":"https://orcid.org/0000-0002-7317-2351","observed_orcids":["https://orcid.org/0000-0002-7317-2351"]},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sheibani, Marjan","raw_affiliation_strings":["Department of Mathematics , Hangzhou Normal University , Hang -zhou , China","Women's University of Semnan (Farzanegan) , Semnan , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hangzhou Normal University , Hang -zhou , China","institution_ids":["https://openalex.org/I163151501"]},{"raw_affiliation_string":"Women's University of Semnan (Farzanegan) , Semnan , Iran","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I163151501"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9897000193595886,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9897000193595886,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.0010999999940395355,"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/generalized-drazin-inverse","display_name":"generalized Drazin inverse","score":0.7910000085830688},{"id":"https://openalex.org/keywords/commutators","display_name":"commutators","score":0.4050000011920929},{"id":"https://openalex.org/keywords/banach-algebras","display_name":"Banach algebras","score":0.8769999742507935},{"id":"https://openalex.org/keywords/idempotents","display_name":"idempotents","score":0.37299999594688416}],"concepts":[{"id":"https://openalex.org/C2777795832","wikidata":"https://www.wikidata.org/wiki/Q4521948","display_name":"Drazin inverse","level":3,"score":0.941202700138092},{"id":"https://openalex.org/C2781106287","wikidata":"https://www.wikidata.org/wiki/Q806066","display_name":"Banach algebra","level":3,"score":0.8111132383346558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8007529973983765},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.707145094871521},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6750227212905884},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.5128238797187805},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4975173771381378},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4689309895038605},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4527651071548462},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33153659105300903},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.29577648639678955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07081273198127747},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2001.00328","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00328","pdf_url":"https://arxiv.org/pdf/2001.00328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2001.00328","doi":"https://doi.org/10.48550/arxiv.2001.00328","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.00328","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.00328","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00328","pdf_url":"https://arxiv.org/pdf/2001.00328","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997679552.pdf","grobid_xml":"https://content.openalex.org/works/W2997679552.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1964879244","https://openalex.org/W2397011395","https://openalex.org/W2556114549","https://openalex.org/W2604745343","https://openalex.org/W2605013721","https://openalex.org/W2614479948","https://openalex.org/W2885949544","https://openalex.org/W2905831414","https://openalex.org/W2933029821","https://openalex.org/W2949094963","https://openalex.org/W2962962401","https://openalex.org/W2990524384"],"related_works":["https://openalex.org/W2933029821","https://openalex.org/W4396871225","https://openalex.org/W4410187618","https://openalex.org/W4407062815","https://openalex.org/W4412078807","https://openalex.org/W4416073873","https://openalex.org/W4394983721","https://openalex.org/W4398789767","https://openalex.org/W2307194520","https://openalex.org/W4283661073"],"abstract_inverted_index":{"Let":[0],"$n\\in":[1],"{\\Bbb":[2],"N}$.":[3],"An":[4],"element":[5],"$a\\in":[6],"R$":[7,17],"has":[8,33,43],"generalized":[9,34,44],"n-strongly":[10,35,45],"Drazin":[11,36,46],"inverse":[12,37],"if":[13,38,41],"there":[14],"exists":[15],"$x\\in":[16],"such":[18],"that":[19,31],"$xax=x,":[20],"x\\in":[21],"comm^2(a),":[22],"a^n-ax\\in":[23],"R^{qnil}.$":[24],"For":[25],"any":[26],"$a,b\\in":[27],"R$,":[28],"we":[29],"prove":[30],"$1-ab$":[32],"and":[39],"only":[40],"$1-ba$":[42],"inverse.":[47],"Extensions":[48],"in":[49],"Banach":[50],"algebra":[51],"are":[52],"also":[53],"obtained.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-01-10T00:00:00"}
