Prime ideal theorem for double Boolean algebras
Léonard Kwuida · Discussiones Mathematicae - General Algebra and Applications · 2007
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).