{"title":"Weighted w-core inverses in rings","authors":"Liyun Wu, Huihui Zhu","doi":"10.21136/CMJ.2022.0134-22","DOIUrl":null,"url":null,"abstract":"Let R be a unital *-ring. For any a, s, t, v, w ∈ R we define the weighted w-core inverse and the weighted dual s-core inverse, extending the w-core inverse and the dual s-core inverse, respectively. An element a ∈ R has a weighted w-core inverse with the weight v if there exists some x ∈ R such that awxvx = x, xvawa = a and (awx)* = awx. Dually, an element a ∈ R has a weighted dual s-core inverse with the weight t if there exists some y ∈ R such that ytysa = y, asaty = a and (ysa)* = ysa. Several characterizations of weighted w-core invertible and weighted dual s-core invertible elements are given when weights v and t are invertible Hermitian elements. Also, the relations among the weighted w-core inverse, the weighted dual s-core inverse, the e-core inverse, the dual f-core inverse, the weighted Moore-Penrose inverse and the (v, w)-(b, c)-inverse are considered.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"581 - 602"},"PeriodicalIF":0.4000,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/CMJ.2022.0134-22","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let R be a unital *-ring. For any a, s, t, v, w ∈ R we define the weighted w-core inverse and the weighted dual s-core inverse, extending the w-core inverse and the dual s-core inverse, respectively. An element a ∈ R has a weighted w-core inverse with the weight v if there exists some x ∈ R such that awxvx = x, xvawa = a and (awx)* = awx. Dually, an element a ∈ R has a weighted dual s-core inverse with the weight t if there exists some y ∈ R such that ytysa = y, asaty = a and (ysa)* = ysa. Several characterizations of weighted w-core invertible and weighted dual s-core invertible elements are given when weights v and t are invertible Hermitian elements. Also, the relations among the weighted w-core inverse, the weighted dual s-core inverse, the e-core inverse, the dual f-core inverse, the weighted Moore-Penrose inverse and the (v, w)-(b, c)-inverse are considered.