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Polars and annihilators in representable DRl-monoids and MV-algebras. (English) Zbl 0986.06008
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.

MSC:
06D35 MV-algebras
06F05 Ordered semigroups and monoids
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