Filters, Ideals and Congruences on Double Boolean Algebras

摘要

Double Boolean algebras (dBas) are algebras D:= (D; ∩, ∪, ﹁, 」, ⊥,〒 ) of type (2, 2,1,1,0, 0), introduced by R. Wille to capture the equational theory of the algebra of protoconcepts. Boolean algebras form a subclass of dBas. Our goal is an algebraic investigation of dBas, based on similar results on Boolean algebras. In these notes, we describe filters, ideals and congruences, and show that principal niters as well as principal ideals of dBas form (non necessary isomorphic) Boolean algebras.