New characterization of $(b,c)$-inverses through polarity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912033789706240 |
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| author | Laghmam, Btissam Zguitti, Hassane |
| author_facet | Laghmam, Btissam Zguitti, Hassane |
| contents | In this paper we introduce the notion of $(b,c)$-polar elements in an associative ring $R$. Necessary and sufficient conditions of an element $a\in R$ to be $(b,c)$-polar are investigated. We show that an element $a\in R$ is $(b,c)$-polar if and only if $a$ is $(b,c)$-invertible. In particular the $(b,c)$-polarity is a generalization of the polarity along an element introduced by Song, Zhu and Mosić [14] if $b=c$, and the polarity introduced by Koliha and Patricio [10]. Further characterizations are obtained in the Banach space context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New characterization of $(b,c)$-inverses through polarity Laghmam, Btissam Zguitti, Hassane Rings and Algebras 15A09, 16W10, 16U60, 47A05 In this paper we introduce the notion of $(b,c)$-polar elements in an associative ring $R$. Necessary and sufficient conditions of an element $a\in R$ to be $(b,c)$-polar are investigated. We show that an element $a\in R$ is $(b,c)$-polar if and only if $a$ is $(b,c)$-invertible. In particular the $(b,c)$-polarity is a generalization of the polarity along an element introduced by Song, Zhu and Mosić [14] if $b=c$, and the polarity introduced by Koliha and Patricio [10]. Further characterizations are obtained in the Banach space context. |
| title | New characterization of $(b,c)$-inverses through polarity |
| topic | Rings and Algebras 15A09, 16W10, 16U60, 47A05 |
| url | https://arxiv.org/abs/2409.11987 |