FP-injectivity relative to a semidualizing bimodule. (Q2915400)
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scientific article; zbMATH DE number 6083233
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | FP-injectivity relative to a semidualizing bimodule. |
scientific article; zbMATH DE number 6083233 |
Statements
17 September 2012
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covers
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envelopes
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precovers
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preenvelopes
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semidualizing bimodules
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\(C\)-FP-injective modules
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right injective dimension
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FP-injectivity relative to a semidualizing bimodule. (English)
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The notion of \(C\)-injective modules is extended to that of \(C\)-FP-injective modules. A result on the (pre)covering and (pre)enveloping properties of \(C\)-FP-injective modules is obtained. Then right \(C\)-FP-injective dimension of modules is studied via right derived functor \(\Hom\). As applications, a necessary and sufficient condition of semidualizing modules having finite FP-injective dimension and a new characterization of left Noetherian rings are provided.
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