On regular elements in an incline. (Q979000)
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scientific article; zbMATH DE number 5726448
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On regular elements in an incline. |
scientific article; zbMATH DE number 5726448 |
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On regular elements in an incline. (English)
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25 June 2010
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Summary: Inclines are additively idempotent semirings in which products are less than (or) equal to either factor. Necessary and sufficient conditions for an element in an incline to be regular are obtained. It is proved that every regular incline is a distributive lattice. The existence of the Moore-Penrose inverse of an element in an incline with involution is discussed. Characterizations of the set of all generalized inverses are presented as a generalization and development of regular elements in a *-regular ring.
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additively idempotent semirings
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regular inclines
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Moore-Penrose inverses
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inclines with involution
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generalized inverses
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regular elements
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