When divisibility by an element implies invertibility. (Q2477961)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When divisibility by an element implies invertibility. |
scientific article |
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When divisibility by an element implies invertibility. (English)
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14 March 2008
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The main result of the article is: A ring is a local ring with nil maximal ideal if and only if multiplication by a non-invertible element of a ring is never a surjection on a non-zero right module (Theorem 2.4). The proof is short and elementary.
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local rings
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nil maximal ideals
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surjections
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invertibility
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right multiplication maps
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homogeneous maps
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