Multiplicative Mappings of Rings
| Autor: | Fang Yan Lu, Jin Hai Xie |
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| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | Acta Mathematica Sinica, English Series. 22:1017-1020 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-005-0620-7 |
| Popis: | Let ℛ and \({\fancyscript S}\) be arbitrary associative rings. A mapping φ of ℛ onto \({\fancyscript S}\) is called a multiplicative isomorphism if φ is bijective and satisfies φ(xy) = φ(x)φ(y) for all x, y ∈ ℛ. In this short note, we establish a condition on ℛ, in the case where ℛ may not contain any non–zero idempotents, that assures that φ is additive, which generalizes the famous Martindale's result. As an application, we show that under a mild assumption every multiplicative isomorphism from the radical of a nest algebra onto an arbitrary ring is additive. |
| Databáze: | OpenAIRE |
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