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Orthogonal decompositions of MV-spaces
Full text linkA maximal disjoint subset of an -algebra is a basis iff is a linearly ordered subset of for all . Let \Spec A be the set of the prime ideals of with the usual spectral topology. A decomposition \Spec A = \cup_{i \in I} T_{i} \cup X
is said to be orthogonal iff each is compact open and is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no with open, , int ) iff is a basis. Many results are established for semisimple -algebras, which are the algebraic counterpart of Bold fuzzy set theory
The stable topology for MV-algebras
No full textLike happens in the commutative rings with unit and in the bounded distributive lattices, the pure ideals of A are characterized via the closed subsets of the hull-kernel topology of Max A, the space of the maximal ideals of A. Opens and stable opens of Max A coincide. Some classes of MV-algebras are also described in terms of their pure ideals
On generalizing the Nullstellensatz for MV algebras
No full textIn this article, first we generalize from the MV algebra [0,1] to an arbitrary MV algebra A the well-known Galois connection (V,I) between the powerset of each power of [0,1] and the powerset of the corresponding free MV algebra. Then, in analogy with the Nullstellensatz of classical algebraic geometry, we study the closure operators obtained by composing the functors V and I
Geometric issues in the algebraic theory of many valued logics.
No full textWe apply to MV-algebras the theory of Universal Algebraic Geometry
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