# Orthogonal decompositions of MV-spaces.

L. Peter Belluce; Salvatore Sessa

Mathware and Soft Computing (1997)

- Volume: 4, Issue: 1, page 5-22
- ISSN: 1134-5632

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topBelluce, L. Peter, and Sessa, Salvatore. "Orthogonal decompositions of MV-spaces.." Mathware and Soft Computing 4.1 (1997): 5-22. <http://eudml.org/doc/39101>.

@article{Belluce1997,

abstract = {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.},

author = {Belluce, L. Peter, Sessa, Salvatore},

journal = {Mathware and Soft Computing},

keywords = {Espacio topológico; Algebras; Algebras semisimples; Descomposición; Lógica multivaluada; Ideal primo; Sistema ortogonal; orthogonal decomposition; annihilator ideals; MV-algebra; basis; prime ideals; semisimple; atomic},

language = {eng},

number = {1},

pages = {5-22},

title = {Orthogonal decompositions of MV-spaces.},

url = {http://eudml.org/doc/39101},

volume = {4},

year = {1997},

}

TY - JOUR

AU - Belluce, L. Peter

AU - Sessa, Salvatore

TI - Orthogonal decompositions of MV-spaces.

JO - Mathware and Soft Computing

PY - 1997

VL - 4

IS - 1

SP - 5

EP - 22

AB - 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.

LA - eng

KW - Espacio topológico; Algebras; Algebras semisimples; Descomposición; Lógica multivaluada; Ideal primo; Sistema ortogonal; orthogonal decomposition; annihilator ideals; MV-algebra; basis; prime ideals; semisimple; atomic

UR - http://eudml.org/doc/39101

ER -

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