A characterization of potent rings
| Autor: | Greg Oman |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Glasgow Mathematical Journal. :1-4 |
| ISSN: | 1469-509X 0017-0895 |
| DOI: | 10.1017/s0017089522000325 |
| Popis: | An associative ring R is called potent provided that for every $x\in R$ , there is an integer $n(x)>1$ such that $x^{n(x)}=x$ . A celebrated result of N. Jacobson is that every potent ring is commutative. In this note, we show that a ring R is potent if and only if every nonzero subring S of R contains a nonzero idempotent. We use this result to give a generalization of a recent result of Anderson and Danchev for reduced rings, which in turn generalizes Jacobson’s theorem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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