Left dual $(b,c)$-core inverses in rings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912170310107136 |
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| author | Calci, Tugce Pekacar Soycan, Serhat Emirhan |
| author_facet | Calci, Tugce Pekacar Soycan, Serhat Emirhan |
| contents | Let $a,b,c\in R$ where $R$ is a $*$-ring. We call $a$ \textit{left dual $(b,c)$-core invertible} if there exists $x\in Rc$ such that $bxab=b$ and $(xab)^*=xab$. Such an $x$ is called a left dual $(b,c)$-core inverse of $a$. In this paper, characteriztions of left dual $(b,c)$-core invertible element are introduced. We characterize left dual $(b,c)$-core inverses in terms of properties of the left annihilators and ideals. Moreover, we prove that $a$ is left dual $(b,c)$-core invertible if and only if $a$ is left $(b,c)$ invertible and $b$ is \{1,4\} invertible. Also, properties of left dual $(b,c)$-core invertible elements are examined. We present the matrix representations of left dual $(b,c)$-core inverses by the Pierce decomposition. Furthermore, reletions between left dual $(b,c)$-core inverses and the other generalized inverses are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Left dual $(b,c)$-core inverses in rings Calci, Tugce Pekacar Soycan, Serhat Emirhan Rings and Algebras 15A09, 16W10, 16U90 Let $a,b,c\in R$ where $R$ is a $*$-ring. We call $a$ \textit{left dual $(b,c)$-core invertible} if there exists $x\in Rc$ such that $bxab=b$ and $(xab)^*=xab$. Such an $x$ is called a left dual $(b,c)$-core inverse of $a$. In this paper, characteriztions of left dual $(b,c)$-core invertible element are introduced. We characterize left dual $(b,c)$-core inverses in terms of properties of the left annihilators and ideals. Moreover, we prove that $a$ is left dual $(b,c)$-core invertible if and only if $a$ is left $(b,c)$ invertible and $b$ is \{1,4\} invertible. Also, properties of left dual $(b,c)$-core invertible elements are examined. We present the matrix representations of left dual $(b,c)$-core inverses by the Pierce decomposition. Furthermore, reletions between left dual $(b,c)$-core inverses and the other generalized inverses are given. |
| title | Left dual $(b,c)$-core inverses in rings |
| topic | Rings and Algebras 15A09, 16W10, 16U90 |
| url | https://arxiv.org/abs/2412.19276 |