Valuations of lattice-ordered groups (Q1359033)
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scientific article; zbMATH DE number 1026096
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Valuations of lattice-ordered groups |
scientific article; zbMATH DE number 1026096 |
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Valuations of lattice-ordered groups (English)
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24 June 1997
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The authors study valuations on lattice-ordered groups with values in a lattice of order ideals of the root system of regular subgroups. They use these valuations to obtain new and old results for archimedean extensions and archimedean closures of lattice-ordered groups. In the penultimate section of their paper, they define \(\Delta\)-extensions and \(\Delta\)-closures and derive a variety of new results for them. This comprehensive paper finishes with a list of interesting open questions.
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valuations
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lattice-ordered groups
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order ideals
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root system
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regular subgroups
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archimedean extensions
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archimedean closures
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