Resumen de Orthogonal decompositions of MV-spaces
L. P. Belluce, Salvatore Sessa
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 = Ui in I Ti U X is said to be orthogonal iff each Ti is compact open and S = {ai}i in I is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no Ti = Theta n Y with Theta open, Theta n Y = emptyset, int Y = emptyset) iff S is a basis. Many results are established for semisimple MV-algebras, which are the algebraic counterpart of Bold fuzzy set theory.
