Quasidualizing modules (Q405383)
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scientific article; zbMATH DE number 6340274
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasidualizing modules |
scientific article; zbMATH DE number 6340274 |
Statements
Quasidualizing modules (English)
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5 September 2014
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quasidualizing
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semidualizing
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matlis duality
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Let \(A\) be a commutative noetherian local ring. An \(A\)-module of finite type \(C\) is called semidualizing if the homothety homomorphism \(A \to \)Hom\(_A(C,C)\) is an isomorphism and Ext\(^{>0}_A(C,C)=0\). In this paper the Matlis duals of semidualizing modules are identified as the artinian modules \(M\) such that \(\hat{A} \to \)Hom\(_A(M,M)\) is an isomorphism and Ext\(^{>0}_A(M,M)=0\), where \(\hat{A}\) is the completion of the local ring \(A\). Some properties and variants are also explored.
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