Decidability of the theory of modules over commutative valuation domains (Q866569)
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scientific article; zbMATH DE number 5126409
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decidability of the theory of modules over commutative valuation domains |
scientific article; zbMATH DE number 5126409 |
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Decidability of the theory of modules over commutative valuation domains (English)
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14 February 2007
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A commutative ring \(V\) with unity is said to be a valuation ring if the lattice of ideals of \(V\) is a chain. A valuation ring without zero divisors is called a valuation domain. It is proved that if \(V\) is an effectively given valuation domain such that its value group is dense and archimedean, then the theory of all (unitary) \(V\)-modules is decidable.
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theory of modules
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commutative valuation domain
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decidability
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Ziegler spectrum
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