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 ∩ Y with Theta open, Theta ∩ 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.
@article{urn:eudml:doc:39101,
title = {Orthogonal decompositions of MV-spaces.},
journal = {Mathware and Soft Computing},
volume = {4},
year = {1997},
pages = {5-22},
zbl = {0880.06004},
mrnumber = {MR1463105},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39101}
}
Belluce, L. Peter; Sessa, Salvatore. Orthogonal decompositions of MV-spaces.. Mathware and Soft Computing, Tome 4 (1997) pp. 5-22. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39101/