Abstract: In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.
Keywords: Boolean algebras, modal algebras, Boolean spaces with relations
Classification (MSC2000): 06E25, 03G05
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