Integral closure in MV-algebras.
We study the consequences of assuming on an MV-algebra A that Σnx exists for each x belonging to A.
Orthogonal decompositions of MV-spaces.
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 results are...
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