# Orthogonal decompositions of MV-spaces.

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

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## Abstract

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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.

## How to cite

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Belluce, 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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