Faithfulness and cancellation over Noetherian domains (Q5928668)
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scientific article; zbMATH DE number 1583363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Faithfulness and cancellation over Noetherian domains |
scientific article; zbMATH DE number 1583363 |
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Faithfulness and cancellation over Noetherian domains (English)
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1 April 2001
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stable ring
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strongly faithful ring
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restricted cancellation of ideals
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Noetherian domains
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generalized Dedekind domains
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The authors study Noetherian domains whose torsion-free modules satisfy various properties characteristic of torsion-free abelian groups, in particular Warfield duality. The main theorem proves the equivalence in Noetherian domains of the following properties: 1. Stability; 2. HT-faithfulness (a type of Warfield duality); 3. Strong faithfulness; 4. Restricted cancellation of ideals. NEWLINENEWLINENEWLINEThe authors show that the main theorem fails for generalized Dedekind domains.
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