When every pure ideal is projective (Q2788570)
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scientific article; zbMATH DE number 6543080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When every pure ideal is projective |
scientific article; zbMATH DE number 6543080 |
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When every pure ideal is projective (English)
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19 February 2016
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pure ideal
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cotorsion pair
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homological dimension
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The authors study \(PIP\)-rings, which are the rings with the property that every pure ideal is projective. Among other results, it is proved that the following are equivalent: (1) \(R\) is a \(PIP\)-ring; (2) every \(RD\) ideal of \(R\) is projective; (3) every pure ideal of \(R\) is pure projective; (4) every cyclic flat \(R\)-module has projective dimension less or equal than \(1\). For a \(PIP\)-ring, the authors give some new homological dimensions for complexes. They also obtain some new characterizations of von Neumann regular rings and semisimple Artinian rings.
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