Prime ideal theorem for double Boolean algebras
Léonard Kwuida
Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007), p. 263-275 / Harvested from The Polish Digital Mathematics Library
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Double Boolean algebras are algebras (D,⊓,⊔,⊲,⊳,⊥,⊤) of type (2,2,1,1,0,0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under ⊓ (resp. ⊔). A filter F is called primary if F ≠ ∅ and for all x ∈ D we have x ∈ F or x⊲∈F. In this note we prove that if F is a filter and I an ideal such that F ∩ I = ∅ then there is a primary filter G containing F such that G ∩ I = ∅ (i.e. the Prime Ideal Theorem for double Boolean algebras).

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:276866 
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Léonard Kwuida. Prime ideal theorem for double Boolean algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 263-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1130/

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