Article
| Title: | Weighted $w$-core inverses in rings (English) |
| Author: | Wu, Liyun |
| Author: | Zhu, Huihui |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 581-602 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a unital $\ast $-ring. For any $a,s,t,v,w\in R$ 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 $a\in R$ has a weighted $w$-core inverse with the weight $v$ if there exists some $x\in R$ such that $awxvx=x$, $xvawa=a$ and $(awx)^*=awx$. Dually, an element $a\in R$ has a weighted dual $s$-core inverse with the weight $t$ if there exists some $y\in R$ 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. (English) |
| Keyword: | inverse along an element |
| Keyword: | $\{e, 1, 3\}$-inverse |
| Keyword: | ${\{f, 1, 4}\}$-inverse |
| Keyword: | weighted Moore-Penrose inverse |
| Keyword: | $(v,w)$-$(b,c)$-inverse |
| Keyword: | $w$-core inverse |
| Keyword: | dual $v$-core inverse |
| MSC: | 06A06 |
| MSC: | 15A09 |
| MSC: | 16W10 |
| idZBL: | Zbl 07729525 |
| idMR: | MR4586912 |
| DOI: | 10.21136/CMJ.2022.0134-22 |
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| Date available: | 2023-05-04T17:50:38Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151675 |
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