On w-Neat Rings
In this paper, we offer a new generalization of the neat ring that is called a w-neat ring. A ring $ R $ is said to be weakly clean if every $ r\in R $ can be written as $ r=u+e $ or $ r=u-e $ where $ u\in$ U$(R) $ and $ e\in$ Id$(R) $. We define a w-neat ring to be one for which every p...
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| Format: | Article |
| Language: | English |
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University of Kashan
2023-03-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_113766_9174f06d418c8dc1d065ce2e54b7a344.pdf |
| Summary: | In this paper, we offer a new generalization of the neat ring that is called a w-neat ring. A ring $ R $ is said to be weakly clean if every $ r\in R $ can be written as $ r=u+e $ or $ r=u-e $ where $ u\in$ U$(R) $ and $ e\in$ Id$(R) $. We define a w-neat ring to be one for which every proper homomorphic image is weakly clean.We obtain some properties of w-neat rings. |
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| ISSN: | 2476-4965 |