Generalized inverses and their relations with clean decompositions
An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e an...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://hdl.handle.net/1822/64193 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/64193 |
| Summary: | An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that an = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n. Also, the existence of the Moore-Penrose and group inverses is related to the existence of certain - clean decompositions. |
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