Polars and annihilators in representable DRl-monoids and MV-algebras (Q2777522)
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scientific article; zbMATH DE number 1717387
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polars and annihilators in representable DRl-monoids and MV-algebras |
scientific article; zbMATH DE number 1717387 |
Statements
7 March 2002
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DRl-monoid
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MV-algebra
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prime ideal
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polar
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Polars and annihilators in representable DRl-monoids and MV-algebras (English)
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MV-algebras are algebraic structures reflecting the infinite-valued Łukasiewicz propositional logic. The category of MV-algebras is equivalent to a subcategory of the dually residuated lattice-ordered commutative monoids (DRl-monoids). This paper studies the connexion between prime ideals and polars of an MV-algebra and the corresponding notions in the associated DRl-monoid. The main result characterizes the linearly ordered ideals in a representable DRl-monoid in terms of minimal prime ideals or of minimal polars.
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