The radical approach to infinitesimals in historical perspective (Q2908633)
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scientific article; zbMATH DE number 6077030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The radical approach to infinitesimals in historical perspective |
scientific article; zbMATH DE number 6077030 |
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5 September 2012
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infinitesimals
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division rings
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Jacobson radical
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0.9007299
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0.9007299
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0.8970895
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0.88638556
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0.86739963
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The radical approach to infinitesimals in historical perspective (English)
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In this interesting paper the author discusses a variety of notions of infinitesimal, sketching along the way the historical development of the concept. He focuses in particular on the ``logical'' definition of infinitesimal originally proposed by Jacques Penon, namely, an element of an (intuitionistic) division ring which is not unequal to zero. The central result of the paper is that the set of Penon infinitesimals in a division ring \(R\) coincides both with the set of non-units of \(R\) and with the Jacobson radical of \(R\).
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