Rings decomposed into direct sums of J-rings and nil rings
Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of thi...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000230 |
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| Summary: | Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of this result, the main theorem of [1] follows. |
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| ISSN: | 0161-1712 1687-0425 |