On Matlis dualizing modules (Q1608218)
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scientific article; zbMATH DE number 1779150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Matlis dualizing modules |
scientific article; zbMATH DE number 1779150 |
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On Matlis dualizing modules (English)
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12 August 2002
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A ring \(R\) has a Matlis dualizing module if there is a faithfully balanced \((R,R)\)-bimodule \(E\) such that \(_RE\) and \(E_R\) are both injective cogenerators. In the reviewer's book `Rings with Morita duality' [Lect. Notes Math. 1523, Springer (1992; Zbl 0790.16009)], this is called a Morita self-duality. The authors prove that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible \((R,R)\)-bimodules and show by example that this number can be greater than one.
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Matlis dualizing modules
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reflexive modules
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faithfully balanced bimodules
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injective cogenerators
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Morita dualities
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invertible bimodules
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