Some remarks on star operations and the class group (Q1106889)
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scientific article; zbMATH DE number 4063228
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on star operations and the class group |
scientific article; zbMATH DE number 4063228 |
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Some remarks on star operations and the class group (English)
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1988
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This paper gives a result concerning when for a fixed star operation * on a commutative ring R, ACC holds for integral *-ideals. - A second theorem shows that two *-ideals are equal if they are equal at certain localizations. That theorem is then used to show that in the domain D, if S is a multiplicatively closed subset generated by principal primes, then \(Pic(D)\to Pic(D_ S)\) and \(Cl_ t(D)\to Cl_ t(D_ S)\) are both injective. (Here, \(Cl_ t(D)=T(D)/\Pr in(D)\), and T(D) is the group of t-invertible t-ideals, the t-operation being a well known star- operation.)
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Picard group
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class group
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star operation
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ACC
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principal primes
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0.8605606
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0.8355911
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0.83290344
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0.8307879
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0.8260465
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