A note on graded NP-rings and graded PS-rings (Q2743103)
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scientific article; zbMATH DE number 1651079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on graded NP-rings and graded PS-rings |
scientific article; zbMATH DE number 1651079 |
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24 September 2001
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graded NP-rings
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graded PS-rings
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projective modules
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socles
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smash products
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0.90282583
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0.8985325
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A note on graded NP-rings and graded PS-rings (English)
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Let \(G\) be a finite group. A \(G\)-graded ring \(R\) is a (graded) NP-ring if each (graded) non-singular left \(R\)-module is (graded) projective, and is a (graded) PS-ring if its (graded) socle is (graded) projective. The authors prove that if \(R\) is strongly \(G\)-graded and \(|G|\) is invertible in \(R\) then the following are equivalent: (1) \(R\) is a NP-ring; (2) the smash product \(R\#G\) is an NP-ring; (3) \(R\) is a graded NP-ring. Similar results hold for PS-rings.
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