On forward-order law for core inverse in rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911099175043072 |
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| author | Kumar, Amit Mishra, Debasisha |
| author_facet | Kumar, Amit Mishra, Debasisha |
| contents | If $a$ and $b$ are a pair of invertible elements, then $ab$ is also invertible and the inverse of the product $ab$ satisfying
$$(ab)^{-1}=a^{-1}b^{-1}$$ is known as the {\it forward-order law}.
This article establishes a few sufficient conditions of the forward-order law for the core inverse of elements in rings with involution. It also presents the forward-order law for the weighted core inverse and the triple forward-order law for the core inverse. Additionally, we discuss the hybrid forward-order law among the Moore-Penrose inverse, the group inverse, and the core inverse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11909 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On forward-order law for core inverse in rings Kumar, Amit Mishra, Debasisha Rings and Algebras 15A09, 16W10, 16B99 If $a$ and $b$ are a pair of invertible elements, then $ab$ is also invertible and the inverse of the product $ab$ satisfying $$(ab)^{-1}=a^{-1}b^{-1}$$ is known as the {\it forward-order law}. This article establishes a few sufficient conditions of the forward-order law for the core inverse of elements in rings with involution. It also presents the forward-order law for the weighted core inverse and the triple forward-order law for the core inverse. Additionally, we discuss the hybrid forward-order law among the Moore-Penrose inverse, the group inverse, and the core inverse. |
| title | On forward-order law for core inverse in rings |
| topic | Rings and Algebras 15A09, 16W10, 16B99 |
| url | https://arxiv.org/abs/2205.11909 |