Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003220220501Residuated lattices derived from filters(ideals) in double Boolean algebras254514766810.52547/HATEF.JAHLA.3.2.3ENT. JeufackYannick LeaUniversity of Yaound´e 1, Faculty of Sciences, Department of Mathematics, Laboratory of Algebra, P.O. Box 812, Yaound´e, Republic of CameroonD.JosephUniversity of Yaound´e 1, Faculty of Sciences, Department of Mathematics, Laboratory of Algebra, P.O. Box 812, Yaound´e, Republic of CameroonE. A.TemgouaEcole Normale Sup´erieure de Yaound´e, Department of Mathematics, CameroonJournal Article20220407Double Boolean algebras (dBas) are algebraic structures D = (D, v, ^, , ', ⊥, T) of type (2, 2, 1, 1, 0, 0), introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Our goal is an algebraic investigation of dBas, based on similar results on Boolean algebras. In this paper, first we characterize filters on dBas as deductive systems and we give many characterization of primary filters(ideals). Second, for a given dBa, we show that the set of its filters F(D) (resp.ideals I(D)) is endowed with the structure of distributive pseudo-complemented lattices, Heyting algebras and residuated lattices. We finish by introducing the notions of annihilators and co-annihilators on dBas and investigate some relalted properties of them. We show that pseudo-complement of an ideal I (filter F) is the annihilator I* of I ( co-annihilator F*) and the set of annihilators (co-annihilators) forms a Boolean algebra. http://jahla.hatef.ac.ir/article_147668_6df71ee93581fe74427beecd82efd9e2.pdf