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Topological MV-algebras. (English) Zbl 0896.06010

The author gives the concept of a topological MV-algebra and studies its completion under the \(I\)-adic topology, \(I\) being a proper ideal of the MV-algebra. Several properties of this topology are studied, like Hausdorffness and completeness, pointing out the corresponding algebraic properties. These results parallel those for topological rings, but these are substantially different because an MV-algebra is not a ring. Relationships between the \(I\)-adic topology and fuzzy ideals are also studied.
Reviewer: S.Sessa (Napoli)

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
22A30 Other topological algebraic systems and their representations
06B30 Topological lattices
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