2011 / March Volume 6 No.1
On prime spectrums of 2-primal rings
| Published Date |
2011 / March
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|---|---|
| Title | On prime spectrums of 2-primal rings |
| Author | |
| Keyword | |
| Download | |
| Pagination | 73-84 |
| Abstract | A $2$-primal ring is one in which the prime radical is exactly the set of nilpotent
elements. A ring is clean, provided every element is the sum of a unit and an idempotent. Keith Nicholson introduced clean rings in 1977 and proved the following: ``Every clean ring is an exchange ring. Conversely, every exchange ring in which all idempotents are central, is clean.'' In this paper, we investigate some of the relationships among ring-theoretic properties and topological conditions, such as a $2$-primal weakly exchange ring and its prime
spectrum Spec$(R).$
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| AMS Subject Classification |
13A15, 06F25
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| Received |
2009-11-17
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| Accepted |
2009-11-17
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