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Orthogonal decompositions of MV-spaces

  • Autores: L. P. Belluce, Salvatore Sessa
  • Localización: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, ISSN-e 1134-5632, Vol. 4, Nº. 1, 1997, págs. 5-22
  • Idioma: inglés
  • Títulos paralelos:
    • Descomposiciones ortogonales de espacios MV
  • Enlaces
  • Resumen
    • 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.


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