Finite nilpotent rings are not dualizable (Q5950772)
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scientific article; zbMATH DE number 1682622
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite nilpotent rings are not dualizable |
scientific article; zbMATH DE number 1682622 |
Statements
Finite nilpotent rings are not dualizable (English)
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16 December 2001
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It was shown by R. Willard in 1996 that the ring \(\mathbb{Z}_4\) is dualizable. A similar result for \(\mathbb{Z}_8\) was obtained by L. Sabourin. The author generalized these results previously for finite commutative rings which are dualizable if and only if their Jacobson radical is a zero ring. In this paper he shows that any finite ring having a nilpotent subring is not dualizable.
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algebraic dualities
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finite rings
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nilpotent rings
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Jacobson radical
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