Generalized inverses of a sum with a radical element (Q1087609)
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scientific article; zbMATH DE number 3987471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized inverses of a sum with a radical element |
scientific article; zbMATH DE number 3987471 |
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Generalized inverses of a sum with a radical element (English)
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1986
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Given a von Neumann regular element a and an element j in the Jacobsen radical J(R) of a ring R with unity, this paper gives necessary and sufficient conditions for \(a+j\) to be von Neumann regular. Moreover, the Moore-Penrose invertibility and group invertibility of the element \(a+j\) are considered. An application is given to matrices over semiprimary SBI rings.
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von Neumann regular element
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Jacobsen radical
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Moore-Penrose invertibility
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group invertibility
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SBI rings
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