EP-like properties of \((b, c)\)-inverses (Q6046081)
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scientific article; zbMATH DE number 7686032
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | EP-like properties of \((b, c)\)-inverses |
scientific article; zbMATH DE number 7686032 |
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EP-like properties of \((b, c)\)-inverses (English)
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15 May 2023
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In this paper, the author defines the $(b, c)$-inverse $y$ of $a$ in any semigroup $S$ for any three elements $a, b, c \in S$ and $y\in S$. He also proves the pairwise implications among $ya = ay$ and other ``EP-like'' properties among elements of $S$. Further, some of them are disproved with relevant counterexamples. The results are powerful and a list of updated references is given at the end of the paper.
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\((b, c)\)-inverse
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Bott-Duffin inverse
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EP matrix
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generalized inverse
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Moore-Penrose inverse
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normal matrix
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pseudo-inverse
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semigroup
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star-dagger property
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