Displaying similar documents to “Maximal and essential ideals of MV-álgebras.”

Molecules and linerly ordered ideals of MV-algebras.

C. S. Hoo (1997)

Publicacions Matemàtiques

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We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B(A) where B(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime. ...

Orthogonal decompositions of MV-spaces.

L. Peter Belluce, Salvatore Sessa (1997)

Mathware and Soft Computing

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A maximal disjoint subset S of an MV-algebra A is a basis iff {x in A : x ≤ a} is a linearly ordered subset of A for all a in S. Let Spec A be the set of the prime ideals of A with the usual spectral topology. A decomposition Spec A = U T U X is said to be orthogonal iff each T is compact open and S = {a} is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no T = Theta ∩ Y with Theta open, Theta ∩ Y = emptyset, int Y = emptyset) iff S is a basis. Many...