The dual of a finitely generated multiplication module (Q1094468)
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scientific article; zbMATH DE number 4025560
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The dual of a finitely generated multiplication module |
scientific article; zbMATH DE number 4025560 |
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The dual of a finitely generated multiplication module (English)
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1989
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Let R be a commutative ring with 1, M a finitely generated unitary (right) R-module, and \(M^ *\) the dual module of M. Let \(D=ann(ann(M))\), and assume that M is a multiplication module. The following are the main results of the paper: 1. \(M^ *\) is finitely generated iff D is finitely generated (f.g.). 2. If D is f.g., then \(M^ *\) is a multiplication module iff D is a multiplication ideal. 3. \(Trace(M)=D\).
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dual module
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multiplication module
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