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
  • Texto completo (pdf)
• 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.