TY - JOUR
ID - 147668
TI - Residuated lattices derived from filters(ideals) in double Boolean algebras
JO - Journal of Algebraic Hyperstructures and Logical Algebras
JA - JAHLA
LA - en
SN - 2676-6000
AU - Yannick Lea, T. Jeufack
AU - Joseph, D.
AU - Temgoua, E. A.
AD - University of Yaound´e 1, Faculty of Sciences, Department of Mathematics, Laboratory of Algebra, P.O. Box 812, Yaound´e, Republic of Cameroon
AD - Ecole Normale Sup´erieure de Yaound´e, Department of Mathematics, Cameroon
Y1 - 2022
PY - 2022
VL - 3
IS - 2
SP - 25
EP - 45
KW - Double Boolean algebra
KW - Filter
KW - ideal
KW - primary
KW - protoconcepts
DO - 10.52547/HATEF.JAHLA.3.2.3
N2 - Double 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.
UR - http://jahla.hatef.ac.ir/article_147668.html
L1 - http://jahla.hatef.ac.ir/article_147668_6df71ee93581fe74427beecd82efd9e2.pdf
ER -